Jurgen Klopp's side recorded a 2-1 win in the first leg at Anfield on January 10 and were just about able to finish the job in the English capital to set up an intriguing final with Chelsea, who beat Middlesbrough 6-2 on aggregate, with the two sides set to lock horns at Wembley on February 25.
Luis Diaz sent Liverpool ahead in the 11th minute of the contest before Issa Diop levelled in the 77th minute, but Marco Silva's side could not find another, with Liverpool triumphing 3-2 on aggregate in the semi-final.
The early danger signs were there for Fulham, as Diaz headed a free kick just wide of the goal inside the first two minutes, and the hosts were simply unable to keep hold of the ball during a disappointing start.
Darwin Nunez was next to try his luck in the sixth minute, with the forward forcing Fulham goalkeeper Bernd Leno into a decent save, before there was a big chance down the other end, with Joao Palhinha, who found himself unmarked inside the box, volleying over the crossbar from a dangerous corner.
Fulham were improving, but they took a huge blow in the 11th minute, with Diaz's whipped effort taking a deflection before beating Leno, who might have felt that he should have kept it out, with Liverpool taking a 3-1 lead on aggregate in the last-four tie.
Liverpool had the ball in the back of the net once again in the 28th minute, with Diaz converting from close range after Nunez had struck the post, but the offside flag was raised.
Diaz was involved again in the 31st minute, testing Leno with a strike, before Liverpool goalkeeper Caoimhin Kelleher made a smart stop down the other end to deny Raul Jimenez.
Kelleher was then forced to keep out an effort from Willian during a strong period for Fulham, who also had a penalty shout when Jimenez went down inside the box, but Liverpool entered the break with a 1-0 lead on the night, leaving them 3-1 ahead in the tie.
Liverpool had a half-chance early in the second period, with Harvey Elliott firing wide of the post after a cross from Diaz, who might have taken the shot on himself.
Both teams then had chances in the 55th minute, with Andreas Pereira striking against the post after Kelleher had failed to deal with Willian's ball into the box, before Elliott fired at Leno down the other end.
Leno made another smart stop just before the hour to deny Nunez, before the Liverpool striker missed the target with a powerful drive from inside the box four minutes later.
Fulham were back in the match in the 77th minute, with Diop converting a cross from Harry Wilson, who brought energy and quality to the home side's attack upon his introduction off the bench.
Wilson then tested Kelleher in the 80th minute, with the hosts firmly on the front foot and needing just one goal to level the scores at 3-3, but it was not to be for Fulham, with Liverpool setting up a final against Chelsea at the end of next month.
Both teams will now switch their attention to the fourth round of the FA Cup, with Fulham hosting Newcastle United on Saturday evening before Liverpool welcome Norwich City on Sunday afternoon.