On days like this there is no need for Tottenham Hotspur to worry about how they will cope without Harry Kane on the pitch. Christian Eriksen demonstrated why he is so much more than a member of the supporting cast as he scored another two splendid goals, taking his tally for the season to 11, to ease Spurs into the FA Cup semi-finals at the expense of a Swansea City side that never turned up.

It was that sort of afternoon for Spurs, who were as comfortable as it gets as they strolled into the last four of the FA Cup for the second year in succession. Eriksen accepted the freedom of the Liberty Stadium given to him by Swansea to score his seventh and eighth goals against the Welsh club in 10 matches – one would have thought they would have learned their lesson by now – and Érik Lamela effortlessly stroked home Tottenham’s second.

In truth the margin of victory could easily have been wider, such was the chasm in quality between the two teams. At times it was embarrassingly one-sided, with Swansea so passive and Spurs utterly dominant as they kept the ball for long periods and attacked with menace. Mauricio Pochettino’s side registered 24 attempts on goal compared with Swansea’s three, enjoyed 75% of possession and had the game wrapped up with the best part of half an hour remaining when Eriksen scored his second.

The Dane was a joy to watch – he had another superb effort tipped on to the crossbar – and Swansea found themselves overwhelmed in midfield, unable to stem the tide of blue shirts that poured forward again and again. Lamela, playing behind Son Heung-min, who was given the nod up front ahead of Fernando Llorente, also enjoyed himself as Spurs made the most of the space afforded to them by a severely depleted Swansea side. “I think we fully deserved the victory,” said Pochettino. “Christian and Lamela shined, of course. But I think the whole team was very good.”

The only source of frustration for Pochettino was the use of VAR, which came into play when Son was flagged offside after scoring in the first half. Even after watching the incident again and again it was hard to call but the original decision was eventually allowed to stand. “It’s a nightmare,” Pochettino said. “I feel so sorry for the people trying to use that system. I think I prefer it when the ref and assistant make mistakes, rather than to wait three or four minutes for things.”

While Spurs can now look forward to a semi-final at Wembley, their temporary home, next month, Swansea’s focus must return to the grind of the relegation battle and trying to preserve their Premier League status. This was only their third defeat in 17 games since Carlos Carvalhal was appointed manager but it was a chastening experience and with the exception of Alfie Mawson, who has just been called up to the England squad, it was hard to think of anyone who emerged with credit.

Tammy Abraham, who started up front in place of the suspended Jordan Ayew, squandered a gilt-edged chance to pull a goal back within 60 seconds of the restart, when he headed straight at Michel Vorm from six yards out, and that moment felt symptomatic of his and Swansea’s afternoon.

Érik Lamela steers home to double Tottenham’s lead. Photograph: Daniel Leal-Olivas/AFP/Getty Images

Spurs were already two goals to the good at that point, with Eriksen having opened the scoring in the 11th minute. Swansea’s defending left much to be desired as they allowed Eriksen, after swapping passes with Lamela, to stride forward towards the edge of the penalty area without coming under any pressure. Yet there was still much to admire about the way the midfielder curled a lovelyleft-foot shot beyond Kristoffer Nordfeldt.

Tottenham’s second goal was not dissimilar and this time it was Lamela who did the damage. Running on to a pass from Moussa Sissoko, the Argentinian skipped away from a half-hearted Tom Carroll challenge and, with Kyle Bartley backing off, coolly placed a low shot past the stranded Nordfeldt and into the bottom corner.

Eric Dier’s long-range effort was expertly clawed behind by Nordfeldt after Abraham had missed that chance but the goalkeeper was powerless to prevent Eriksen from drilling home his second to turn Swansea’s first FA Cup quarter-final since 1964 into a damp squib. “There came a storm today,” Carvalhal said. “But after a storm there will be good weather.”