Liverpool turned in a vintage display on a ground which has twice seen them win the European Cup.
Two second-half Michael Owen goals secured Liverpool a priceless two-goal advantage to take home to Anfield in a week's time.
But it was a determined and defiant team performance which provided the foundations for a famous win.
42 mins: Rinaldi's cross finds Delvecchio but the Roma captain wastes the first chance of the game as he heads wide
47 mins: Owen stuns the home fans with the opening goal, cutting out Rinaldi's attempted pass and firing beyond Antonioli
64 mins: Roma sub Assuncao sees his stinging shot beaten away by Westerveld
65 mins: Roma play their trump card, throwing on striker Batistuta
71 mins: Ziege's cross finds Owen in space and he flicks home a header for his second
89 mins: Barmby's clever run opens up the Roma defence but his shot is blocked by the legs of Antonioli
Roma had been beaten on their own ground in a dramatic penalty shoot-out in the 1984 European Cup final and Liverpool fans are beginning to treat the Stadio Olympico as a spiritual home.
The travelling fans taunted the home crowd with chants of "We always win in Rome" as Liverpool established themselves as firm favourites to secure a quarter-final clash with either Nantes or Porto.
Owen, who has been struggling for fitness for weeks, made his first start in eight games.
But when he made way for Jari Litmanen late in the second half, the ovation he received from the Liverpool fans provided noisy confirmation that this 21-year-old striker is far from the spent force that many had claimed.
It was Owen who made the breakthrough within two minutes of the second half.
Having doggedly restricted Roma to just one first-half chance, when Marco Delvecchio headed over from an Alessandro Rinaldi cross, Liverpool were keen to make their own chances count.
This time, Rinaldi was the villain, attempting a suicidal cross field pass too close to his own penalty area.
Owen was quick to sniff the chance and cut out the pass before clinically firing a shot beyond helpless keeper Antonioli.
The home side were rocked and quickly set about trying to repair the damage they had caused themselves.
Sander Westerveld was alert enough to beat away a shot from substitute Assuncao and Fabio Capello was quick to increase his goalscoring chances by throwing on dangerman Gabriel Batistuta.
The Argentine striker had not been considered fit enough to play twice in a week, but Roma had looked punchless without him.
But, within two minutes of his arrival, Owen ensured it was he and not Batistuta who would grab the headlines.
Christian Ziege, having seen his free kick cleared, was given a second chance to cross and this time the Roma defence was undone.
Owen exploited the space mercilessly, stealing in ahead of goalkeeper Antonioli to glance home the faintest of headers.
Liverpool's defence grew meaner as they became hungrier and Roma were a well-beaten side by the final whistle.
It could have been even more painful for the home side as Barmby skipped past a defence appealing in vain for an offside which was never given.
Barmby suddenly had a glorious chance to continue his record of a goal in every Uefa Cup away tie Liverpool have played this season, but saw his impressive run ended by the legs of Antonioli.
A third goal would have been more than Liverpool boss Gerard Houllier could have dreamed of, and there was no hiding his delight at the final whistle.
"The whole team was superb," he cried.
"I was worried because we had players missing through injury and others cup tied, while there were several playing who were only just back from injury.
"But Michael's goals gave us confidence and the defence was outstanding."
Owen was delighted to make a goalscoring return and said: "It is nice to play in such a great stadium and to come away with two goals.
"It was a great performance by the whole team."
Roma: Antonioli, Rinaldi, Samuel, Mangone, Cafu, Emerson, Tommasi, Nakata, Montella, Delvecchio, Candela.
Subs: Lupatelli, Assuncao, Di Francesco, Guigou, D'Agostino, Batistuta, Balbo.
Liverpool: Westerveld, Babbel, Henchoz, Carragher, Ziege, Hyypia, Barmby, Hamann, McAllister, Fowler, Owen.
Subs: Vignal, Litmanen, Diomede, Wright, Navaro, Smicer, Arphexad.
Referee: Markus Merk (Kaiserslautern)
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