The five-times European champions, who will confront holders Real Madrid in the May 26 last, twice led the pack yet were compelled to hold tight in the second half as Roma made shots previously Radja Nainggolan's two late objectives put them ahead on the night.
Liverpool's Sadio Mane was their most powerful assaulting danger and gave them the lead following nine minutes, yet an odd claim objective by James Milner leveled for Roma.
A Georginio Wijnaldum header set Liverpool back in front however Roma, who toppled a three-objective shortage to beat Barcelona in the last round, were given recharged conviction when Edin Dzeko terminated past Loris Karius ahead of schedule in the second half.
Nainggolan penetrated in from separate following 86 minutes to make it 3-2 and crushed home a punishment in stoppage-time however it was past the point of no return for the Italian side who lost the principal leg of the semi-last 5-2 in Liverpool.
"We never do it the easy way sadly," Liverpool chief Jordan Henderson said. "It was an astonishing exertion. In the primary half we did well and scored some great objectives. General we dealt with the circumstance well separated from the most recent 10 minutes."
Liverpool's errand was apparently direct - abstain from affliction a three-objective thrashing and a place in the last in Kiev was theirs.
Their 5-2 first-leg triumph at Anfield was a scoreline that had never been toppled in the opposition's history, however Barcelona's stun crush in a similar stadium had filled in as a notice against lack of concern.
The group positively appeared to trust a rehash result was conceivable and the commotion levels expanded as Liverpool were pushed back in the opening minutes.
However Roma's spirits were hosed when Liverpool led the pack, gaining by a cataclysmic mix-up with a normally clinical counter.
Roma midfielder Nainggolan played a self-destructive square ball that was jumped on by Roberto Firmino, who drove forward and played it through to Mane who covered his left-footed complete past Roma's Brazilian attendant Alisson.
That was the main objective Roma had yielded at home in the opposition this season, yet they were behind for six minutes because of a catastrophic claim objective.
Dejan Lovren endeavored to clear a ball into the region yet crushed his exertion straight into the substance of Milner and it ricocheted past Karius.
The home fans rediscovered their voice, yet their reestablished spirits kept going just an additional 10 minutes before Liverpool retook the lead.
The hosts neglected to clear a corner and the ball was going back by Dzeko into the way of Wijnaldum who gestured past Alisson.
Roma leveled for the second time seven minutes after the break as Stephan El Shaarawy's shot was pushed gently into the way of Dzeko by Karius and the Bosnian rifled his complete past the German attendant.
It was then all out of options for the Premier League side as Roma chances went back and forth before Nainggolan focused from the edge of the zone and rifled a shot in off the post.
He pummeled home a punishment after substitute Ragnar Klavan was declared to have taken care of, however it was insufficient to anticipate Liverpool achieving the last out of the blue since 2007.