Paul Scholes was sent off as Roma left Manchester United battling to keep their Champions League ambitions alive.
Scholes saw red after 33 minutes for fouls on Christian Wilhelmsson and Francesco Toto in a quarter-final first leg marred by crowd trouble.
Rodrigo Taddei's deflected shot put Roma ahead after 44 minutes.
Wayne Rooney coolly scored his first Champions League goal since 2004, but Mirko Vucinic slid in Roma's second after 66 minutes for a slender lead.
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United recalled Ole Gunnar Solskjaer up front, but he struggled to make an impact as the Premiership leaders failed to assert themselves in the first half.
And their task was made even harder by the foolishness of Scholes, who was deservedly sent off for two rash challenges.
He went into the book after 25 minutes for a late tackle on Wilhelmsson and was dismissed eight minutes later for tripping Totti.
It was all the incentive Roma needed to try and push home their advantage, with Taddei firing narrowly wide.
But he made no mistake a minute before half-time when United were caught cold by a short corner.
Totti played in Mancini, and his ball across the box was turned in by Taddei via the legs of Wes Brown.
The interval was marred by ugly scenes of violence involving supporters from both sides and Italian police.
When the action resumed, it was Roma who were again in the ascendancy, Taddei bringing a smart save from Edwin van der Sar and Totti firing just over.
But United, never a side to take the easy option when the difficult route is still open to them, defied the odds to equalise on the hour.
Van der Sar's throw released the outstanding Cristiano Ronaldo, who surged forward to feed Solskjaer.
He crossed for Rooney, who chested down before finishing in style high past Doni.
Roma's confidence was dented, and Doni needed to be alert to save from Ronaldo.
But just as United appeared to have finally established a measure of control, Roma sprang forward to regain the lead.
Van der Sar pushed out Mancini's shot tamely, and substitute Vucinic slid home the rebound.
Roma pushed for a crucial third, and Simone Perrotta volleyed over at the far post after good work from Totti.
The dangerous Totti then fired inches wide as United looked in danger of conceding again.
Roma: Doni, Panucci, Mexes, Chivu, Cassetti, Wilhelmsson (Vucinic 62), Taddei (Rosi 82), De Rossi, Perrotta, Mancini, Totti.Subs Not Used: Curci, Faty, Defendi, Ferrari, Okaka Chuka.
Booked: Perrotta.
Goals: Taddei 44, Vucinic 67.
Man Utd: Van der Sar, Heinze, Ferdinand, O'Shea, Brown, Ronaldo, Giggs (Saha 77), Carrick, Scholes, Rooney, Solskjaer (Fletcher 72).Subs Not Used: Kuszczak, Smith, Dong, Richardson, Eagles.
Sent Off: Scholes (34).
Booked: Scholes, Solskjaer, Heinze.
Goals: Rooney 60.
Att: 77,000
Ref: Herbert Fandel (Germany).