(Liverpool win 7-6 on aggregate)
Liverpool reached the Champions League final after riding their luck to contain a fired-up AS Roma in defeat at the Stadio Olimpico that sent them through 7-6 on aggregate.
Liverpool, who will face Real Madrid in the final on 26 May, twice took the lead but were forced to hang on in the second half as Roma created a string of good chances before Radja Nainggolan's two late goals put them ahead on the night.
Liverpool's Sadio Mane was their most potent attacking threat and gave them the lead after nine minutes, but a bizarre own goal by James Milner levelled for Roma.
A Georginio Wijnaldum header put Liverpool back in front but Roma, who overturned a three-goal deficit to beat Barcelona in the last round, were given renewed belief when Edin Dzeko fired past Loris Karius early in the second half.
Nainggolan drilled in from distance after 86 minutes to make it 3-2 and smashed home a penalty in stoppage-time but it was too late for the Italian side who lost the first leg of the semi-final 5-2 in Liverpool.
Jurgen Klopp's side are smashing all kinds of records this season and another one fell as they reached 46 goals in 14 Champions League matches (including qualifiers), eclipsing the previous best set by Barcelona (in 16 games) in 1999-2000.
A great deal of that is owed to their formidable front three of Mohamed Salah (10), Roberto Firmino (10) and Mane (nine), now the highest scoring club trio in a single Champions League season after overtaking Real Madrid's Cristiano Ronaldo, Gareth Bale and Karim Benzema, who scored 28 in 2013-14.
They are the fastest to 40 (12 matches) in a single campaign in the competition proper.
It was Mane's turn to star on the night Liverpool booked their first Champions League final place in 11 years and their eighth in the competition.
Having survived a scare when Alessandro Florenzi fired a long-range shot just wide Mane, who had an early penalty claim waved away after Kostas Manolas' challenge, struck the first blow which severely damaged Roma's hopes of clawing back the first-leg deficit.
Naingollan squandered possession in midfield and Jordan Henderson fed Firmino, who teed up his team-mate for a smart left-footed finish: the first goal conceded by Roma at home in the Champions League this season as Liverpool maintained their record of scoring in every away fixture.
That left the hosts requiring four in 81 minutes and they were handed a lifeline when Dejan Lovren, under pressure from Patrik Schick, hacked the ball straight at Milner's head and rebounded past goalkeeper Loris Karius.
Liverpool wobbled and Roma sensed their chance but that was taken away from them by a second away goal, cancelling out the only slight advantage the Serie A side had coming into the tie, in the 25th minute.
Alisson turned Mane's shot for a corner after Andrew Robertson's driving 35-yard run to the byline to provide Wijnaldum with his big moment, heading in his first away goal in 1,081 days since he found the net for PSV Eindhoven against Den Haag in May 2015 and his first for an English club in 64 away games.
It sent the 5,000 travelling fans, who had to deal with long queues to get in but apparently none of the pre-match security concerns, into raptures.
Stephan El Shaarawy offered Roma hope as he had a shot deflected off Milner and onto the post and a penalty shout against Trent Alexander-Arnold turned down but when Dzeko fired home a badly-directed punch from Karius, Roma required three in 38 minutes to force extra-time.
Alexander-Arnold appeared to get away with a handball against El Shaarawy but Liverpool were hanging on even before Nainggolan's 86th-minute drilled effort off the post set nerves jangling, with the midfielder converting a penalty after substitute Ragnar Klavan's handball.
Klopp told BT Sport 2: "The boys deserve it. The campaign, the character they showed, the mentality they showed, the football they showed - that's just crazy.
"And then it suits our situation, what was it? On aggregate it's - I forgot it - 7-6, it was unbelievable."
The German added: "To be honest, there's a lot of room for improvement in our general defending.
"We were constantly under pressure. Each counter attack was really dangerous but we didn't use them, we are usually much better. We wanted to do it, without doing the right thing.
"It was the first semi-final for most of the boys and it's completely normal that you have to keep your nerves and all of that stuff.
"It was a little bit exciting, more exciting than what I actually want but now it's over and I'm fine."
Liverpool skipper Jordan Henderson said: "We never do it the easy way, unfortunately. Amazing effort. We knew it'd be tough coming here.
"I thought in the first half, we did well and scored some good goals. We could have been a bit more clinical on the counter attack but overall I thought we handled the situation well, apart from the last 10 minutes of the second half - and concede the late goals like we did - so we need to stop that but overall we're delighted to be in the final.
"We knew it was important to get that first goal and to get one early on was brilliant.
"A little bit unlucky with their first goal. But overall, first leg, second leg, I think we're going to be happy with what we've done.
"Of course, we could have been a lot better here in this leg, but overall we're just pleased to get through to the final. We've been entertaining I think."
Ex-Liverpool captain Steven Gerrard was quick to congratulate his former team.
"Incredible achievement, congratulations to Jurgen Klopp and the players - they're the ones that have taken the fans on this journey," Gerrard said.
"They deserve all the plaudits they'll get in the coming days.
"They've set themselves up for a mouth-watering final against Real Madrid and they should go in with confidence they can go all the way now. That man (Klopp) and the players deserve so much praise."