Champions League - Rooney at the double for United
Rooney coolly converted a 64th minute penalty to ease the growing tension at the Stadionul National before Nemanja Vidic was shown a rather harsh red card in what was a nervy and unconvincing display from the English champions.
The match was levelled up numerically as Milan Perendija was shown a second yellow card late on, and there was still time for Rooney to double his tally from the penalty spot as the forward gave his side a crucial victory.
Sir Alex Ferguson made nine changes from the side which drew with Liverpool at the weekend as Rooney was handed a starting berth in attack and Vidic returned for his first start since August 14.
Under normal circumstances, a trip to face the ailing Romanian champions, sandwiched in between key Premier League fixtures against Liverpool and Manchester City would be the cue for Ferguson to rest many of his senior players but, after squandering a two-goal lead against Basle at Old Trafford three weeks ago, this was a match United desperately needed to win.
It was a subdued start from United, and the first chance of the match fell to Galati forward Ionut Neagu in the 15th minute, who almost capitalised on a sloppy piece of play from Fabio to drive a low shot on target from the edge of the area, but Anders Lindegaard dived to his right to save.
There was a real scare for United four minutes later as Lindegaard hammered an attempted clearance straight into the back of Vidic, who stood flat-footed in front of him, but fortunately for the visitors the ball fell to safety.
United's best chance of the first half fell to Michael Carrick, who produced a shoddy effort to side-foot the ball over the crossbar from inside the Galati box following fine work from Nani down the left.
Ferguson no doubt handed out a resplendent rollicking at the break after a sluggish first half, and the tempo of United's play was noticeably quicker from the restart with greater urgency in the visitors' advances.
A flurry of bookings awarded in rather haphazard fashion by referee Dr Felix Brych caused the play to be fragmented, and United grew increasingly frustrated with the onus on the visitors to dictate affairs.
Rooney went close to breaking the deadlock in the 63rd minute as he swivelled sharply to turn Cornel Rapa after latching on to Evra's cut back, but his shot fizzed narrowly wide of the far post with Grahovac at full stretch.
But just seconds later, United were presented with their breakthrough opportunity as Galati captain Sergiu Costin inexplicably handled in his own box to give the visitors a penalty.
Rooney duly lashed home the spot kick to give United the lead, and in so doing racked up his 10th goal in his last 15 Champions League ties as he looked to alleviate some of the tension from his side's ranks.
But just two minutes later, there was further drama as referee Brych brandished what appeared to be an extremely harsh red card to give Vidic a straight red card for a lunging, but fairly innocuous clearance.
Before United could send on Jonny Evans to replace Antonio Valencia, Liviu Antal really should have levelled the scores as the Galati winger blasted a wild volley over the crossbar from inside the United box after Carrick failed to clear.
United suddenly looked to be in disarray as Galati unleashed wave after wave of pressure, and substitute Marius Pena was afforded a free header inside the visitors' box after no one managed to deal with Sorin Frunza's cross, but he could not hit the target.
A late onslaught of pressure from the hosts did not yield an equaliser, but Bratislav Punosevac went very close with a volley from the edge of the United box after collecting Filip's cross in his stride, only to see his effort zip agonisingly wide of the near post.
The ever-combative Perendija was shown a second yellow card for a cynical tug on Hernandez three minutes from time, and the German referee seized the opportunity to level the match up numerically before Nani struck the post with a speculative drive in the dying moments.
But there was still time for Rooney to win another penalty as he was too fleet of foot for Antal - who tripped him crudely inside the box - and the forward again beat Grahovac with a clinical finish to double his personal tally and seal the result.
It was an extremely testing victory for United and, considering the English champions' squad cost £241m compared to the £500,000 required to assemble the group of Galati players, the result will have come as a surprising relief to Ferguson ahead of the crunch Manchester derby at the weekend.