Rooney coolly stroked home a 64th-minute penalty and a further spot-kick in injury time to give the English giants a vital three points in Group C after draws with FC Basel and Benfica in their opening two fixtures.
The result left United second in the standings with three matches still to play, trailing group leaders Benfica by two points.
The Portuguese side, who still have to travel to Old Trafford, were comfortable victors at Basel in the night's other fixture.
But victory came at a cost for Sir Alex Ferguson and United, who saw fit-again captain Nemanja Vidic -- making his first start for the club since the opening game of the season -- given a straight red card.
A lacklustre first half finished goal-less, with United controlling possession but failing to make their dominance count.
Galati by contrast were forced to live off scraps, although the Romanian champions grew in confidence as the half wore on.
Ioan Filip caused flutters in the United defence on 27 minutes, embarking on a mazy gallop into the penalty area before sending a rasping shot just over.
At the other end, United's best chance came from a 30th minute free-kick from Rooney, the England international's 25-yard curler being parried away by Galati keeper Branko Grahovac.
Galati continued to probe for openings however and Liviu Antal probably should have done better than direct his header over on 44 minutes after out-jumping Patrice Evra in the area.
United came out for the second half with a renewed sense of purpose, and almost got their breakthrough when Nani picked out Rooney in the penalty area only for the striker to screw his shot just wide.
The United fans did not have long to wait for the opener however, and it came on 64 minutes from the penalty spot.
Galati captain Sergiu Costin needlessly slapped at a cross from Rooney inside the area, leaving German referee Felix Brych no choice but to award the spot-kick.
Rooney duly stepped up to make it 1-0 and calm United's nerves, but Ferguson's men were forced to endure a nervous final 25 minutes when Vidic was dismissed for a late tackle on Gabriel Giurgiu.
Vidic's challenge was late and high but the Serbian seemed stunned as Brych brandished a straight red when most observers in Bucharest's National Stadium had appeared to be expecting a yellow.
Galati however were unable to make their numerical advantage count, and were themselves reduced to 10 men in the closing minutes when Vidic's fellow Serb defender Milan Perendija was sent off.
Then in injury time as Rooney was tripped by Antal inside the area to earn a second penalty which he calmly slotted in the same corner.