Jurgen Klopp's side headed to the Italian capital with a commanding 5-2 advantage from last week's first leg, where their Serie A opponents snatched faint hopes of a comeback by netting a pair of late away goals.
Still, Roma had no margin for error – certainly not to the magnitude of the woeful blind pass midfielder Radja Nainggolan played in the ninth minute that resulted in Sadio Mane opening the scoring.
An incredibly unfortunate James Milner own goal did not knock Liverpool off their stride, with Georginio Wijnaldum restoring their ample cushion in the 25th minute.
First-leg goalscorer Edin Dzeko got in on the act seven minutes into the second half and frantic Roma pressure followed.
The mountain proved too steep for Eusebio Di Francesco's side to climb and the chances of a comeback to match their quarter-final heroics against Barcelona had all but evaporated by the time Nainggolan clattered in off the post four minutes from the end and dispatched a penalty deep into stoppage time.
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It was a predictably forthright start from the hosts as Dzeko sent the ball skidding dangerously across the six-yard box before Alessandro Florenzi clattered a long-range effort just wide.
But Nainggolan's mistake allowed Liverpool to further strengthen their hand, with Roberto Firmino collecting a wayward pass and streaming towards the home defence.
The Brazil international played in Mane, who showed none of his first-half skittishness from the opening leg and finished assuredly.
Following that act of self-sabotage, Roma then enjoyed a huge slice of fortune as Dejan Lovren thumped a 15th-minute clearance into Milner's head for the ball to fly past a helpless Loris Karius.
The Stadio Olimpico crowd were re-energised, but chances continued to fall Liverpool and Mane's way – a clipped shot flying just wide from the edge of the box before Alisson denied the Senegal star at close quarters following a driving run from Andrew Robertson.
Dzeko failed to clear from the resulting corner, leaving an unmarked Wijnaldum to nod home and put the tie further beyond Roma.
Stephan El Shaarawy's effort spun off Milner's outstretched leg 10 minutes before the break to hit the post and Florenzi sliced wastefully wide, although those were fleeting breaks in Liverpool's first-half control.
Karius was spared by an incorrect offside flag in the 49th minute when he dashed from his goal to bring down Dzeko in the box.
The Liverpool goalkeeper then somewhat charitably pushed El Shaarawy's shot into Dzeko's path for the former Manchester City striker to level on the night.
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Trent Alexander-Arnold was also partially culpable on Roma's second goal, but atoned with a brave block to deny El Shaarawy – even if replays showed the ball struck his hand.
Dzeko's touch let him down and he arrowed a shot wide at the near post following Daniele De Rossi's cleverly disguised 66th-minute pass, while Alisson stuck out a boot to deny his compatriot Firmino on a Liverpool attack that suggested the storm had passed.
Nainggolan's late defiance raged against the inevitable – ripping a low drive in off the post before thrashing in a spot-kick after Liverpool substitute Ragnar Klavan was adjudged to have handled – although it was the Belgian's earlier woe that put Liverpool on the road to Kiev despite their first loss in this season's competition.
Photo Getty Images. Caption: Liverpool's Georginio Wijnaldum celebrates