Ahead 2-1 after the first leg, the Reds took an early lead through Luis Diaz.
Liverpool hung on to confirm their place in the final, though, at the expense of Marco Silva's side, and they will face Chelsea at Wembley.
Dom Smith was at Craven Cottage to take in the action...
One Fulham fan called for Jimenez to tackle Bradley, shouting: "Come on, he's No84, he can't be that good." But he is good. Played well again, except for slightly weak defending that allowed Fulham's leveller.
Virgil van Dijk 7
Won everything in the air and was composed as he distributed the ball to his team-mates.
Jarrell Quansah 7
Turned into Trent Alexander-Arnold for Liverpool's opener, with an inch-perfect flighted ball which landed right onto Diaz's chest.
Did nothing wrong. Continues to do what is asked of him while covering for injuries in the unfamiliar left-back position.
They say it's a sign of a good midfield performance if it is hard to notice the player, but Gravenberch's involvements in this match really were few and far between! Put one sighter wide.
Alex Mac Allister 6
A couple of nice touches in midfield, but made a meal of one challenge from Tom Cairney which was barely a foul.
His excellent first touch gave Liverpool an outlet, allowing the likes of Gravenberch and Mac Allister to play into him and trust his ability to control.
Luis Diaz 8
Alert and up for it from the off, Diaz was Liverpool's star performer and scored the goal which saw them into the final.
Unlucky in front of goal again, Nunez was typically lively and Jurgen Klopp can rely on the Uruguayan to press well too.
Quiet night for the Dutchman. Unable to take a presentable chance early in the second half.
Diogo Jota (Nunez, 67') 5
Never stopped running but came on when Fulham were improving and seeing more of the ball.
Curtis Jones (Mac Allister, 67') 5
Barely involved in proceedings.
Ibrahima Konate (Gakpo, 83') N/A
Bobby Clark (Gravenberch, 84') N/A
Not used: Alisson, Robertson, McConnell, Beck, Nyoni