Match ends, Swansea City 0, Tottenham Hotspur 3.
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 Kane
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.
'A storm came but good weather will follow' - what they said
Swansea manager Carlos Carvalhal: "I am not disappointed, a storm came today, but good weather will follow for us.
"Tottenham are a good side, we needed to be at our best and them not at their best, because everyone knows they are better than us.
"But it is the best cup run since 1964 and we take a lot of positives and must not take anything bad out of the game today.
"My focus is on staying in the Premier League and that does not change. We must completely focus on the Premier League and not think about the cup.
"We have eight cup finals now but they all come for us in the league."
Tottenham manager Mauricio Pochettino: "We are very happy with our performance, I am pleased for the players, and they were excellent.
"There is still a long way to go, we are now in the semi-final and even though we feel we are close, we are far away still.
"We have the opportunity to try and get to the final. Things have changed at Wembley, no? The perception and feeling is different.
"Seven months ago it was horrendous, now we are comfortable and happy to play there."
Swans' rotten record against Spurs - the best of the stats
- Tottenham have reached the FA Cup semi-finals in consecutive seasons for the first time since the 1980-81 and 1981-82 campaigns. They won the competition in both those seasons.
- Swansea are now winless in their last 16 games in all competitions against Tottenham (D3 L13).
- 56% of the home goals Swansea have conceded in all competitions in 2018 have been against Tottenham (5/9).
- Eriksen has had a hand in 13 goals in 10 games against Swansea in all competitions (eight goals, five assists), more than he has against any other opponent for Spurs.
- Four of Eriksen's last six goals for Tottenham in all competitions have been from outside the box, including each of his last three.
- Lamela has had a hand in five goals in five FA Cup games this season (two goals, three assists), compared to just two in 17 Premier League appearances (no goals, two assists).
Man of the Match - Christian Eriksen (Tottenham)
Swansea continue their fight for safety in the Premier League with a tough trip to Old Trafford to face Manchester United on Saturday, March 31 (15:00 BST).
Tottenham's next game is on Sunday, 1 April (16:00 BST) when they travel to Chelsea for an important match in the race for a place in the top four.
- 26NaughtonSubstituted forNarsinghat 45'minutes
- 5van der HoornSubstituted forRobertsat 81'minutes
- 12DyerSubstituted forRoutledgeat 86'minutes
- 4Ki Sung-yueng
- 6D SánchezBooked at 69mins
- 27Lucas MouraSubstituted forLlorenteat 73'minutes
- 11LamelaSubstituted forAlliat 81'minutes
- 7Son Heung-Min
- Kevin Friend
- Shots on Target
Second Half ends, Swansea City 0, Tottenham Hotspur 3.
Corner, Tottenham Hotspur. Conceded by Alfie Mawson.
Attempt blocked. Moussa Sissoko (Tottenham Hotspur) right footed shot from outside the box is blocked. Assisted by Fernando Llorente.
Delay over. They are ready to continue.
Delay in match Tammy Abraham (Swansea City) because of an injury.
Substitution, Swansea City. Wayne Routledge replaces Nathan Dyer.
Corner, Tottenham Hotspur. Conceded by Kyle Bartley.
Attempt blocked. Fernando Llorente (Tottenham Hotspur) left footed shot from the left side of the six yard box is blocked.
Attempt blocked. Fernando Llorente (Tottenham Hotspur) left footed shot from very close range is blocked.
Attempt saved. Christian Eriksen (Tottenham Hotspur) right footed shot from a difficult angle and long range on the left is saved in the centre of the goal.
Ben Davies (Tottenham Hotspur) wins a free kick on the left wing.
Foul by Ki Sung-yueng (Swansea City).
Corner, Tottenham Hotspur. Conceded by Kyle Bartley.
Offside, Swansea City. Martin Olsson tries a through ball, but Luciano Narsingh is caught offside.
Substitution, Tottenham Hotspur. Dele Alli replaces Erik Lamela.
Substitution, Swansea City. Connor Roberts replaces Mike van der Hoorn.
Offside, Swansea City. Sam Clucas tries a through ball, but Tammy Abraham is caught offside.
Foul by Son Heung-Min (Tottenham Hotspur).
Sam Clucas (Swansea City) wins a free kick in the defensive half.