The United forward coolly converted two second-half spot-kicks as returning captain Nemanja Vidic was controversially sent off after the break.
Sir Alex Ferguson’s men failed to click into gear during a rather dull first half before the visitors were handed their chances from 12 yards.
United dominated the opening exchanges in Bucharest as the Romanian champions were largely left chasing shadows by the Red Devils.
But for all their possession, the visitors failed to really test Branko Grahovac in the Galati goal. Michael Carrick squandered what was probably United’s best chance of the half when he sent his shot flying over the crossbar from Nani’s cut-back.
Rooney and Nani both tested Grahovac from distance but despite enjoying over 66 per cent possession before the break, United failed to create any other clear-cut opportunities of note.
Indeed, Galati grew in confidence as the half went on and begin to carve their own half-chances. The best of them fell to Ioan Filip, who sent an ambitious drive over the crossbar.
United made a slow start to the second half, too, with Galati happy to sit back and soak up any attacks.
But the game burst into life on the hour-mark. The first warning sign for the home side came in the 62nd minute, when Nani found Rooney with a low cross from the left. The England striker swivelled on the spot but dragged his shot just wide of the left post.
With the pressure building, the visitors were awarded a penalty when Sergiu Costin handled Rooney’s early cross to Javier HernÃ¡ndez. The 25-year-old coolly slotted the spot-kick past Grahovac to give United the lead in the 64th minute.
Vidic, making his first start for United since August after shaking off a calf injury, was then showed a straight red card for a high tackle on Gabriel Giurgiu.
Replays showed it to be a somewhat harsh decision but German referee Felix Brych did not hesitate in reaching for his pocket, leaving the United centre-half wide-eyed with disbelief.
Galati were reduced to 10 men themselves two minutes from time when Milan Perendija was shown a second yellow card for pulling back HernÃ¡ndez.
Rooney then won another penalty when he was tripped by a careless challenge by Liviu Antal in the 91st minute. The United forward duly stepped up and fired his second spot-kick the same way as his first to double his side’s advantage and net an 11th goal in his last 15 Champions League outings.
The final whistle followed shortly after. Despite sealing their first group stage win – a result that moves them up to second place in Group C – this was not as comfortable a night for United as many had predicted.
“In a lot of these away games you have to work hard to get the victory. In the second half we improved a great deal and I was satisfied with the result. We had a long night – we had to be patient and work our way through the game.
“[Vidic] raised his foot and particularly in Europe I can see why [the referee] has given the red card, but it’s very harsh. I shouldn’t think we’ll appeal.”
Otelul Galati: Branko Grahovac, Adrian Salageanu, Cornel Rapa, Sergiu Costin, Milan Perendija, Ioan Filip, Ionut Neagu (Marius Pena, 72), Sorin Frunza (Silviu Ilie, 83), Liviu Antal, Gabriel Giurgiu, Bratislav Punosevac (Gabriel Viglianti, 87).
Manchester United: Anders Lindegaard, Chris Smalling, Nemanja Vidic, Fabio (Phil Jones, 76), Patrice Evra, Anderson, Antonio Valencia (Jonny Evans, 71), Michael Carrick, Nani, Wayne Rooney, Javier HernÃ¡ndez.
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