Christian Eriksen scored twice as Tottenham reached the semi-finals of the FA Cup for a second successive season with a comfortable win at Liberty Stadium.
Fabulous first-half goals from Eriksen and Erik Lamela set Spurs on their way as they chase a ninth FA Cup win.
Eriksen's second made the result safe just past the hour mark.
Tottenham might even have had the game sewn up by half-time, but Son Heung-min's effort was ruled out for offside after consultation with the video assistant referee (VAR).
Spurs are seeking a first trophy since they won the 2008 League Cup.
Sublime Spurs forget about KaneLamela extends Tottenham's lead
Without a trophy in a decade and now out of contention for the Champions League and Premier League titles, Spurs fans will be forgiven for daring to dream about a first FA Cup success since 1991.
If questions are being asked of Tottenham's ability to deliver silverware, they certainly gave a decisive answer in a truly dominant display at Liberty Stadium.
That was all the more impressive in the absence of their talisman Harry Kane, who is ruled out until April with an ankle injury.
There are few bigger compliments to give Spurs than to say they did not miss Kane - 53 goals in his last 53 matches and all - as they were led by inspirational performances from Eriksen and Lamela.
Swans manager Carlos Carvalhal has spoken before of making the opposition "listen to our music" but Eriksen was the conductor while Lamela, Son Heung-min and Lucas Moura played a sweet symphony, their interchange and movement beguiling Swansea.
Mauricio Pochettino's men should have been out of sight before half-time, but were denied by poor finishing, fine goalkeeping and the woodwork as a procession of chances came their way.
In between Eriksen's sumptuous opener and Lamela's terrific effort on the stroke of half-time, Eriksen thundered the bar, Lucas missed from six yards and Eric Dier flashed a free header over the bar, while the video assistant also denied Tottenham what they thought was a legitimate goal.
However, Eriksen, as he so often does, simply tortured the Swans, pulling the strings as he scored his seventh and eighth goals against the Welsh side in just 10 appearances.
The FA Cup is not a priority for Spurs if you listen to Pochettino, but there can be no doubt Spurs supporters feel differently.
The eight-time winners have lost seven successive semi-finals and have not tasted FA Cup glory for 27 years, the days of Paul Gascoigne and Gary Lineker, but they will be dreaming now, especially as they are so familiar with Wembley.
VAR controversy again in the FA CupReferee Kevin Friend consulted VAR in the first half after Son thought he had scored for Tottenham
But for the technology, Spurs would have been effectively into the semi-finals by half-time.
However, just as it was against Rochdale in the previous round, the issue of VAR was once again at the forefront in the FA Cup and again Tottenham felt aggrieved.
The controversy came on 23 minutes when Son went clean through and crashed the ball home off the underside of the crossbar, only to be denied by the linesman's flag.
Spurs immediately appealed for the decision to be reviewed and despite replays seemingly showing Son to be level, the original verdict was upheld after a lengthy delay.
However, such was the gulf between the sides;the disallowed goal was scarcely a factor in the result.
Tottenham took control after Eriksen's brilliant curled effort gave them the lead on 10 minutes and with the Dane seemingly at the centre of everything and Spurs enjoying an extraordinary amount of possession, the second seemed inevitable.
That it took until first-half stoppage time was a surprise, but after Eriksen and Moura combined, Lamela swept home right-footed.
The contest might have changed if former Swansea keeper Michel Vorm had not brilliantly denied Martin Olsson's firm drive and Tammy Abraham's point-blank follow-up, but Spurs made them pay the price when Eriksen fired home a decisive third after Moura's run just past the hour.
Swansea's priority is very much Premier League survival and they were grateful the scoreline was not more decisive with Spurs a class above but wasteful in front of goal....
Man of the Match - Christian Eriksen (Tottenham)As well as having the most shots of any player in the match (six), Eriksen also created the most goal-scoring opportunities for his team-mates (also six)
Former England captain Michael Vaughan says Kevin Pietersen was the "best batsman I had the pleasure to play with" after his ex-team-mate appeared to announce his retirement.
Pietersen, 37, had been playing for Quetta Gladiators in the Twenty20 Pakistan Super League.
"I'm going to take the same passion and hard work into trying to save rhinos from extinction."
South African-born Pietersen was part of four Ashes victories and briefly captained England, while the former Hampshire and Surrey player starred when the national team won the World T20 title in 2010.
"Not everyone's cup of tea but you will do for me," former England captain Michael Vaughan tweeted. "Best batsman I had the pleasure to play with and the first England batsman that put fear into the Aussies."
The England and Wales Cricket Board also posted a message, saying "thank you" to Pietersen.
Former England team-mate Andrew Flintoff also congratulated him "on an amazing career" and thanked him "for having a positive impact on mine too".Andrew Flintoff and Pietersen were England team-mates
Following the end of his international career, Pietersen predominantly became a globe-trotting T20 specialist, playing in the T20 leagues in Australia, India, South Africa, West Indies and the PSL.
His last appearance in England came for county side Surrey last summer.
|Italy (17) 27|
|Tries:Allan 2, Minozzi Cons:Allan 3 Pens:Allan 2|
|Scotland (12) 29|
|Tries:Brown, Barclay, Maitland, Hogg Cons:Laidlaw 3 Pen:Laidlaw|
Greig Laidlaw's 79th-minute Scotland penalty denied Italy their first Six Nations victory since 2015 in Rome.
Tommaso Allan had booted Italy ahead in a dramatic final 10 minutes, before Laidlaw's decisive strike.
Former Scotland Under-20 fly-half Allan contributed 22 points, including a try in each half, and also set up Matteo Minozzi to touch down.
Fraser Brown, John Barclay, Sean Maitland and Stuart Hogg scored for the Scots, who earned a try bonus point.
Gregor Townsend's men were frequently pedestrian and error-strewn in possession, but battled back from 12 points down in the second half.
Scrum-half Laidlaw's late kick claimed the visitors their first away championship win since beating Italy two years ago.
The Scots have matched their 2017 tally of three wins from five, while winless Italy pick up the wooden spoon.Tommaso Allan scored a try, three conversions and a penalty for Italy
For much of this battle, Scotland were blasted to the high heavens by the explosiveness of the Italians, the rampant ball-carrying of lock Dean Budd and, until they started to fade later on, the colossal back-row trio, Sebastian Negri, Jake Polledri and captain Sergio Parisse.
The great man was on 99 Test defeats and you almost wept for him when 99 became 100.At the end, he stood in shock at what had happened.The one that got away.
Scotland looked buried for so long, seemingly undone by Italian power and their own horrendous error count.Credit to them for digging it out.Credit to Laidlaw for holding his nerve at the death.
The visitors, for long periods, were mistake-ridden, physically dominated, routed at the breakdown and lost in so many ways.After a couple of minutes they coughed up their first line-out and seconds later Huw Jones forced a pass to WP Nel.The chain of blunders went from there.Fraser Brown flopped over for the game's opening try
Allan put Italy ahead with the boot, a score that was wiped out when the Scots showed a rare modicum of accuracy and composure, Hamish Watson throwing a long pass out to the right wing where Brown scooped it up to score.
That, in turn, was matched when Allan cut through a gap left open by Jones to score at the posts.Converting his own try, Italy led 10-5.
The Azzurri had the bit between their teeth.Debutant Polledri carried and carried.Running from deep with a ferocity Scotland couldn't handle, they scored a second try just after the opening quarter.
Its origins lay in Finn Russell kicking out on the full.Italy hit it up - and then struck for glory, the wonderful Allan grubbering beautifully for Minozzi to beat Watson to the touch-down.
For the hugely exciting full-back, it was a fourth try in row in this Six Nations.With the conversion, Italy now led 17-5.To that point, they had 78% possession and had forced Scotland into making 78 tackles.It was Cardiff, and the Scots' opening-day humiliation at the hands of Wales, revisited.Matteo Minozzi sprinted onto Tomasso Allan's kick to score Italy's second try
They showed they still had a pulse when a monster maul - and how significant the maul was to prove for the Scots - allowed Barclay to go over to narrow the gap to five.
Scotland were steeped in luck that it remained a five-point game at the break for Italy looked to all the world that they'd scored again just before half-time.No matter.They scored just after half-time instead.
Two minutes into the new half, having turned Scotland over yet again and after Negri had battered through Jonny Gray, it looked like they'd scored a third try.
Negri was celebrating when the TMO was consulted and the try ruled out for a Giulio Bisegni knock-on.It was a lucky break for Scotland, but they couldn't lift the siege.Sean Maitland's try helped propel the Scottish comeback
Zander Fagerson's spilled ball, Ryan Wilson's missed tackle on Polledri, Laidlaw's flailing miss on the same rampaging forward got the hosts in behind Scotland.Polledri gave it to Allan and away he went.Try, conversion, Italy ahead 24-12.
Italy blew a golden overlap soon after and, finally, Scotland stirred.Another maul, a long skip pass from Laidlaw and Maitland was over in the corner.
With 10 minutes left, a 35m maul and a lot of patience gave Hogg a gap to run through - and run through it he did.Laidlaw added the extras and Scotland had hit the front, 26-24.
The endgame was hugely dramatic.With five minutes left, after Jonny Gray was penalised on the floor, Allan put over the kick to inch Italy back into a one-point lead.Stuart Hogg scampered clear to bag Scotland's fourth try and the bonus point
With one minute left, after the home side collapsed a maul, Laidlaw had his seismic moment out on the right.
His kick was high and true and life-saving.Scotland had pulled it from the fire.The cruellest of cruel days for Italy.For Scotland, a deeply sobering experience but a third win of the season - and blessed relief.
|6 (1)||Scrums won (lost)||4 (0)|
|7 (0)||Line-outs won (lost)||12 (2)|
|107 (5)||Rucks/mauls won (lost)||125 (3)|
|27||Kicks from hand||27|
|149 (19)||Tackles made (missed)||158 (15)|
Italy: Minozzi, Benvenuti, Bisegni, Castello, Bellini, Allan, Violi;Lovotti, Ghiraldini, Ferrari, Zanni, Budd, Negri, Polledri, Parisse (capt).
Replacements:Fabiani (for Ghiraldini, 77), Quaglio (for Lovotti, 59), Pasquali, Steyn (for Zanni, 53), Licata (for Polledri, 67), Palazzani (for Violi, 67), Canna (for Castello, 74), Hayward (for Benvenuti, 59).
Scotland: Hogg, Seymour, Jones, Grigg, Maitland, Russell, Laidlaw, Reid, Brown, Nel, Swinson, J Gray, Barclay (capt), Watson, Wilson.
Replacements:McInally (for Brown, 40), Bhatti (for Reid, 40), Fagerson (for Nel, 40), Gray (for Swinson, 53), Denton (for Wilson, 67), Price (for Russell, 54), Horne (for Jones, 53), Kinghorn....
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