An eighth-minute goal from Antonio Valencia and a deflected Wayne Rooney shot later ruled an own goal secured the win for United, who now head Group C on goal difference from Benfica with two matches left.
But the win could not disguise a largely unimpressive performance from the English giants, who struggled to break down a stubborn Galati side still looking for their first ever Champions League point.
“They made it difficult for us,” United manager Sir Alex Ferguson said.
“It’s down to us now. It’s a good incentive for us. The history between the two clubs (United and Benfica) is fantastic, so it’ll be a good night.”
United talisman Rooney was unfazed by the below-par display, insisting the result was all.
“We did a job tonight, we had to win,” Rooney told Sky Sports.
“In the Champions League there’s no easy games. People might look and think that they’re not the best team but if they work hard it’s difficult to break them down.”
Ferguson had named an attacking line-up, with Dimitar Berbatov partnering Michael Owen in front of a midfield comprising Nani, Valencia, Anderson and Rooney in an unusual deep-lying role.
And it looked as if a rout could be on the cards when Valencia shot United ahead with the game only a few minutes old.
Berbatov released the overlapping Phil Jones down the right, and the England defender curled in a superb low cross that Owen just failed to touch on before Valencia jabbed home from close range.
Owen’s role in the goal was to be his last meaningful contribution of the night, with the former England striker being substituted on 11 minutes for Javier Hernandez after picking up a thigh injury.
United’s challenge waned over the remainder of the half, however, as Galati regrouped well to frustrate Ferguson’s side, playing their first home match since last month’s 6-1 thrashing by Manchester City.
Fabio brought the crowd to its feet with a stirring individual run that carried the Brazilian full-back from inside his own half into the Galati penalty area but the foray came to nothing.
Jones, by far United’s most threatening player early on, went close on 33 minutes but his curling shot was deflected behind for a corner.
United’s best spell came in the closing minutes of the first half, with the lively Hernandez stretching the visiting team’s back four.
The Mexican livewire was released by Berbatov down the left, only for Galati captain Sergiu Costin to snuff out the danger with a well-timed tackle.
Costin was pressed into action again in the 41st minute, again thwarting Hernandez after a lovely through ball from Rooney.
Yet Galati caused a scare for United in the 42nd minute, when Ionut Neagu pounced on a stray pass from Nani to home in on goal.
The striker’s shot took a wicked deflection off Rio Ferdinand but David de Gea did brilliantly to save one-handed as United breathed again.
United started the second half with more purpose but despite the best efforts of Rooney, the game remained strangely flat.
United’s early pressure almost yielded a goal soon after the restart but Berbatov’s low cross for Anderson was well cut out by keeper Branko Grahovac.
On 58 minutes Anderson and Berbatov combined again to threaten the Galati goal, playing a neat one-two before Anderson dinked his shot beyond Grahovac, only for Costin to scramble the goal-bound effort off the line.
With the clock running down, Rooney made sure of the victory when his shot from outside the area took a big deflection off Cristian Sarghi to beat Grahovac on 87 minutes.