The five-times European champions, who will face holders Real Madrid in the May 26 final, suffered a nerve-shredding second half as the Italians pinned them back and scored twice late on through Radja Nainggolan.
Nainggolan's second, which came from a stoppage-time penalty, moved Roma to within one goal of forcing extra time, but Liverpool, who clinched the last of their titles in 2005, held on to reach their 10th European Cup final.
They were far from their devastating attacking best, however, and a nervy defensive display saw them lose their first match in this season's competition, despite cruising in the first half having twice taken the lead.
Liverpool's Sadio Mane was their most potent attacking threat and put them ahead after nine minutes, but a bizarre own goal by James Milner levelled for Roma.
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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 from the spot but it was too late for the Italian side who lost the first leg of the semi-final 5-2 in Liverpool.
"We are deserved finalists 100 percent," said Liverpool manager Juergen Klopp. "You don’t come without luck. We needed it only one time tonight.
"The boys deserve it, the character they showed, the football they showed -- it was just crazy. I forgot the score. It was 7-6 right? Unbelievable."
Liverpool's task was seemingly straightforward -- avoid suffering a three-goal defeat and a place in the final in Kiev was theirs.
Their 5-2 first-leg victory at Anfield was a scoreline that had never been overturned in the competition's history, but Barcelona's shock defeat in the same stadium had served as a warning against complacency.
The crowd certainly seemed to believe a repeat result was possible and the noise levels increased as Liverpool were pushed back in the opening moments.
CLINICAL COUNTER
Yet Roma's spirits were dampened when Liverpool took the lead, capitalising on a catastrophic mistake with a typically clinical counter.
Roma midfielder Nainggolan played a suicidal square ball that was pounced on by Roberto Firmino, who drove forward and played it through to Mane who buried his left-footed finish past Roma's Brazilian keeper Alisson.
That was the first goal Roma had conceded at home in the competition this season, but they were only behind for six minutes thanks to a calamitous own goal.
Dejan Lovren tried to clear a ball into the area but smashed his effort straight into the face of Milner and it ricocheted past Karius.
The home fans rediscovered their voice, but their renewed spirits lasted only another 10 minutes before Liverpool retook the lead.
The hosts failed to clear a corner and the ball was headed back by Dzeko into the path of Wijnaldum who nodded past Alisson.
Roma levelled for the second time seven minutes after the break as Stephan El Shaarawy's shot was pushed tamely into the path of Dzeko by Karius and the Bosnian rifled his finish past the German keeper.
It was then backs to the wall for the Premier League side as Roma chances came and went before Nainggolan took aim from the edge of the area and rifled a shot in off the post.
He slammed home a penalty after substitute Ragnar Klavan was adjudged to have handled, but it was not enough to prevent Liverpool reaching the final for the first time since 2007.
(Reporting by Toby Davis, editing by Ed Osmond)
