In the absence of the stricken Harry Kane, Spurs needed someone to step up and that is exactly what Eriksen did as he scored a goal either side off Erik Lamela's strike just before half-time to ensure easy progress to the semi-finals for Mauricio Pochettino's side.
On the other hand, the Swans will now have to put all of their focus on Premier League survival as that is the main at the end of the day and they have given themselves a big chance of doing that was recent performances.
Swans went close to opening the scoring in the opening minutes
As was expected, both sides made plenty of changes to their starting elevens for the game and it seemed to benefit the home side early on as they almost took the lead with less than five minutes gone.
Just as Nathan Dyer was about to get his shot away on goal from close range, Michel Vorm came rushing out of his goal to make a crucial block to stop the winger from opening the scoring.
Eriksen struck Spurs into the lead with a brilliant strike
After playing really well in the opening ten minutes of the game though, the Swans were hit by a sucker punch in the 11th minute when a brilliant left-footed strike from Eriksen from outside the box flew into the top corner of the net after Lamela gave him the ball.
That goal really changed the complexion of the game as Spurs took control for the rest of the half and they had the ball in the back of the net again when a brilliant pass from Eriksen found Son Heung-Min through on goal and he put the ball into the back of the net but after some deliberation, VAR agreed with the linesman that the goal shouldn't be allowed due to an offside decision.
Eriksen was really controlling everything for Spurs and he almost added a second goal for Spurs five minutes before half-time when once again the Swans players gave him too much space on the edge of the box, but this time, the Danish midfielder saw his brilliant strike tipped onto the crossbar by Kristoffer Nordfeldt.
Lamela added a second for Spurs on the stroke of half-time
It only delayed the inevitable though as Spurs did get a second goal before the half-time whistle went when Moussa Sissoko gave Lamela the ball and the winger went on a mazy run before curling a right-footed shot into the bottom corner of the net to give Spurs a two-goal cushion at the break.
Therefore, it meant that the Swans had it all to do in the second half of the game to get back into the tie, while Spurs knew if they kept up their good play their was more goals for them in the game.
Vorm's brillance denied Swans from getting back into the game
You could see at the start of the second half that Carlos Carvalhal had words with his Swansea side as they upped their game after the break and if is wasn't a for brilliant double save from Vorm, they would have got a way back into the game.
The first save was from a Martin Olsson thunderbolt from outside the box and the second one was from the rebound as Tammy Abraham saw his header clawed away off the line.
This proved to be a crucial moment in the game as that was the only real chance that a well-drilled Spurs defence gave their hosts and after that scare they stepped it up again in search of a third goal.
Eric Dier went close to getting the third goal after unleashing a great long range strike towards goal which forced Nordfeldt into a very good save.
Eriksen added a third to end the game as contest and send Spurs through to the semi-finals
Moments later though, Spurs did get a third goal. It was no surprise who got the goal either as Eriksen scored his second of the game from just outside the box after Lucas Moura laid the ball off to him to end the game as a contest.
Spurs had further chances to increase their lead before the end of the game as Fernando Llorente, who came on as a second half substitute, saw a shot from and Eriksen free-kick cleared off the line.
The Swans huffed and puffed right to the end of the game to try and get a goal but they lacked the composure of a final pass to get a goal as the game ended in a comfortable win for the Lilywhites, who will now go on to play in the semi-finals at Wembley next month, while the Swans must now put all their focus on Premier League survival until the end of the season.