Antonio Valencia put the home side ahead in the eighth minute when he turned in Phil Jones’ low cross from the right.
But United did not make the points secure until three minutes from time, when Wayne Rooney’s long-range shot took a huge deflection off Cristian Sarghi and flew past Branko Grahovac in the Galati goal.
The victory puts the Red Devils in control of Group C, with Ferguson’s men topping the table and knowing that victory over Benfica at Old Trafford in three weeks will secure their passage to the last 16.
“The win was important,” said Ferguson. “Our opponents defended very well, they pressed the ball everywhere and put some energy into the game tonight which made it difficult for us.
“It’s down to us – if we beat Benfica we’ll win the group. It’s a good incentive for us, being at home on a big night because the history between the two clubs is fantastic.”
Rooney was deployed in central midfield during Wednesday’s clash, and Ferguson heaped praise on the England international following an assured display – but insisted it is not likely to be a long-term arrangement.
“I thought he was fantastic in the centre of midfield,” continued Ferguson. “His awareness of people around him and his choice of passing was very good. He did really well for us tonight.
“We’re just trying to organise the midfield a little better. We’ve had injuries in that department.”
Michael Owen limped off with a thigh injury just 11 minutes into the game – but Ferguson praised the 31-year-old striker for the role he played in United’s opener.
“He made the goal for us,” said Ferguson. “He made a fantastic run to the front post for Phil Jones’s cross and took all the defenders with him and was left for a simple knock-in by Antonio.”
Meanwhile, Rooney insisted he has no issues playing in central midfield on a regular basis.
“It’s no problem,” said Rooney. “I played there a lot when I was younger. If the manager asks me to do it then I’m happy to.
“I’ve said before I feel I’m a good enough footballer to play anywhere on the pitch. I feel I’m capable of doing that so if the manager asks me to I’ve got no problem doing it.”
The 26-year-old added: “We’ve done a job tonight. We knew we had to win. We know there are no easy games in the Champions League and thankfully we got the 2-0 win. If we can win our next home game then I think we’ll win the group.”
Manchester United: David De Gea, Jonny Evans (Ezekiel Fryers, 89), Phil Jones, Rio Ferdinand, Fabio, Anderson (Park Ji-Sung, 80), Antonio Valencia, Nani, Dimitar Berbatov, Michael Owen (Javier HernÃ¡ndez, 11), Wayne Rooney.
Otelul Galati: Branko Grahovac, Adrian Salageanu, Cornel Rapa, Sergiu Costin, Cristian Sarghi, Ioan Filip, Ionut Neagu, Gabriel Giurgiu (Gabriel Paraschiv, 81), Silviu Ilie (Sorin Frunza, 53), Liviu Antal (Laurentiu Iorga, 62), Marius Pena.
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