The reds made it three Champions League wins out of three with a late Valencia goal at the Luzhniki Stadium.
On a better-than-expected plastic pitch, United held their own in tame first half before stepping up their efforts after the break.
Pressure on the CSKA goal mounted steadily throughout the second period and, with just four minutes on the clock, the £17m signing from Wigan struck home the winner after a flick on header from Berbatov.
In the other Group B game, Wolfsburg drew 0-0 with Besiktas, giving United, on nine points, a five-point cushion at the halfway stage.
Watch a post-match interview with Sir Alex Ferguson here.