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.
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 Cup
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.