The Reds held a 5-2 aggregate lead from the first leg at Anfield and were 2-1 up at half time in Rome in the second leg.
However, Jurgen Klopps men conceded three in the second half but held out to ensure they will face Zinedine Zidanes side in the final.
Sadio Mane and Georginio Wijnaldum got Liverpools goals in Italy and it took the clubs tally this season in the Champions League to 46 for the campaign.
Most goals in a Champions League season (including qualifying):
1. Liverpool (17/18) – 46 goals in 14 games
2. Barcelona (99/00) – 45 in 16 games
3. Real Madrid (13/14) – 41 in 13 games
4. Manchester United (02/03) – 37 in 16 games
5. Real Madrid (16/17) – 36 in 13 games
— WhoScored.com (@WhoScored) May 2, 2018
Thats now a Champions League record, meaning Liverpool have overtaken Barcelonas tally of 45 in 16 games in the 1999/2000 season.
Real Madrid now stand between Liverpool and the clubs sixth European Cup.
Zidanes men will be favourites in Kiev to claim their 13th title and their fourth in the last five years but Liverpools dismantling of Roma and Manchester City in the last two rounds will have frightened the La Liga giants.