The Brazilian midfielder stepped inside Wes Brown after Mirko Vucinic had found him on the left and curled the ball into the top corner in 71st minute. Spanish defender Gerard Pique had headed in a Nani corner to put the visitors in front in the 34th. The result does not alter the positions in Group F.
The Premier League champions, who were sure of topping the group before the game and fielded a second-string team, have 16 points while the Serie A side, who had already qualified for the knockout stage in second, are on 11.
After the trouble that marred both quarter-final ties between the two teams last season, there were more clashes among rival supporters. Five United fans and one Roma supporter were stabbed before kickoff, the ANSA news agency reported.
"This is something we hoped would not happen," United manager Alex Ferguson told a news conference. "We hoped for a quiet night with no incidents. I'm disappointed at that. I hope the fans are OK."
Roma had plenty of chances either side of Pique's opener.
Francesco Totti had the ball in the back of the net in the 11th minute but the goal was disallowed as the striker was offside when he latched on to Philippe Mexes's long pass.
Portuguese defender Antunes came close with a cross-cum-shot in the 20th minute, Mauro Esposito glanced the ball wide in the 29th and United's Polish keeper Tomasz Kuszczak produced a great save to keep out Mancini just before the break.
United's biggest scare of the first half came in the 37th minute when Totti rolled the ball to Mancini, who hit the crossbar from short range and Esposito headed the rebound over the bar. The effort would not have counted though, as Totti was offside again.