United are making a habit of securing 1-0 wins this season, but they were made to work hard for the three points against a Roma side who were determined to atone for the 7-1 defeat in the quarter-finals of last season's competition.
Both sides had won their opening group games - United 1-0 at Sporting Lisbon and Roma 2-0 against Dynamo Kyiv, but the first half of the match was very dull with chances at a premium.
In the 20th minute Cristiano Ronaldo blasted a 30-yard free-kick into the centre of the Roma wall but the visitors were proving to be very disciplined, organised and hard to break down.
A rare defensive error by the Serie A side's defence allowed Louis Saha a shot on goal, but the Frenchman's effort was straight at Roma's stand-in keeper Gianluca Curci.
Just past the half-hour Francesco Totti's deflected 30-yard free-kick was gathered by Tomasz Kuszczak at the second attempt, before Nani crossed for Rooney to blast his first-time effort over the bar.
After such a grim opening half, the second period could only get better and so it proved as Totti almost opened the scoring in the 49th minute after being found by Ludovic Giuly only to spoon his close-range shot over the bar.
Nani's error then gifted possession to Roma, but after Giuly and Totti had created the opening, Alberto Aquilani blasted his shot over the bar.
As United responded, Nani's cross-cum-shot rolled along the top of the crossbar with Curci stranded, while Ronaldo's cheeky back-heel was disallowed for a clear offside.
The deadlock was finally broken in the 70th minute as Rooney grabbed his first goal of the season.
The former Everton man took Nani's pass in his stride before driving a crisp shot beyond Curci and into the back of the net off the post.
Roma created two good chances in the closing stages to grab an equaliser.
However, substitute David Pizarro's deflected shot was safely gathered by Kuszczak before, with only two minutes remaining, Totti set up Mauro Espositio who powered a shot inches wide when it looked easier to score.