Portugal forward Ronaldo soared inside the area six minutes before the break to head home a Paul Scholes cross after Rooney had skipped away from Philippe Mexes.
Rooney then poked home the second goal himself in the 66th minute after a header from South Korean midfielder Ji-Sung Park sparked a goal-mouth scramble.
Roma had nothing to show for some fluid football and have a massive task in next week's return at Old Trafford, where it lost 7-1 at the same stage of the competition last season.
The English champion made a shaky start at the Stadio Olimpico and its Dutch goalkeeper Edwin van der Sar was lucky to get away with a risky early clearance.
Roma defender Christian Panucci then headed just over the bar from a corner in the 12th.
United tried to fashion a response but Brazilian midfielder Anderson hoofed their first effort well off target and Ronaldo drilled a long-distance free kick wide.
The hosts continued to look dangerous and Montengro striker Mirko Vucinic hit a powerful strike over the bar but it was Ronaldo who gave United the lead to stun the home fans.
Roma tried to respond and Vucinic squandered a superb chance to equalise with only Van der Sar to beat soon after the goal.
A determined Roma, who was without injured captain Francesco Totti, made a bright start to the second half.
Full-back Max Tonetto come close with a powerful effort and almost surprised Van der Sar with a cross-come-shot, while Panucci blasted over from short range.
Van der Sar produced a superb reflex save from a Vucinic header in the 62nd and United looked to be struggling before Rooney claimed his fourth goal in five games against Roma.
Ronaldo hit the post with a shot from outside the area and midfielder Michael Carrick nearly made it 3-0 with another long-range strike.
Rooney then struck the ball wide from a good position and Ronaldo volleyed just over as the home side began to lose heart in the closing stages.