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With striker Kane sidelined for several weeks due to ankle ligament damage, Mauricio Pochettino’s side received an inspirational performance from Eriksen at the Liberty Stadium.
The midfielder rose to the challenge with a majestic strike to open the scoring early in the first half of the quarter-final.
After Erik Lamela increased Tottenham’s lead before half-time, Eriksen struck again after the interval to make it seven goals in 10 matches against Swansea.
Tottenham, chasing their first silverware under Pochettino, are back in the Wembley semi-finals after losing to Chelsea at that stage of the competition last season.
Pochettino was pleased with the way Tottenham took control without Kane and Dele Alli, who was only a late substitute.
“If you watch the last three games, we won with a different starting eleven and now today too,” he said.
“What is important is that everyone is available to play and the team is not affected by the names. We keep the same way, the same dynamic and that is so important.
“It was a very good performance. We fully deserved the victory. Now, Wembley for the semi-final.”
Swansea never got going on a freezing afternoon in south Wales and can now concentrate on trying to preserve their Premier League status.
Swansea’s only chance to upset the form book came when they had an early appeal for a penalty turned down when Tottenham goalkeeper Michel Vorm upended Nathan Dyer.
But Tottenham were unruffled and quickly settled into a tempo that had the home side outnumbered and second best in midfield.
The visitors went ahead in the 11th minute through a wonderful strike by Eriksen, although Swansea manager Carlos Carvalhal appealed to the fourth official for VAR to overturn it.
Carvalhal felt Martin Olsson had been fouled in the build-up, but there was no debate about the quality of Erikson’s finish as the Dane curled the ball past Kristoffer Nordfeldt from the edge of the box after being set up by Lamela.
– Spurs stroll –
Tottenham forward Son Heung-Min crashed the ball into the net off the underside of the bar in the 23rd minute only for the goal to be ruled out for offside, correctly concluded the officials in charge of the VAR technology.
Eriksen then found himself in space again on the edge of the box, but his curling shot was brilliantly tipped onto the bar by Nordfeldt.
A second goal for Spurs felt inevitable and it arrived on the stroke of half-time.
Once again, Swansea were chasing shadows and when Sissoko played in Lamela the Argentinian skipped past Tom Carroll and calmly passed the ball into the corner of the goal before Nordfeldt had time to move.
Swansea made a change at the break, replacing Kyle Naughton with Luciano Narsingh, but the pattern remain unchanged as Spurs pressed for a third goal.
Tammy Abraham might have pulled a goal back with a rare Swansea opportunity, but when Vorm parried a shot from Olsson, Abraham’s diving header flew straight back to the Spurs keeper.
Nordfeldt then kept his team in the contest with a superb save to turn away Erik Dier’s goal-bound long range effort.
Just past the hour, Spurs sealed the victory.
The hard-working Lucas Moura played the ball back to Eriksen, who claimed a deserved second goal with a low shot from the edge of the box that had sufficient power to go through Nordfeldt’s hands.
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