
Chances had been at a premium on the artificial surface of the Luzhniki Stadium -- scene of United's final victory over Chelsea in 2008 -- but United finished strongly and deserved their win.
Antonio Valencia, who celebrated his first Manchester United goal last weekend, doubled his tally for the club five minutes from time, moments after rattling the crossbar with a fierce drive.
The Ecuador winger Valencia latched onto a downward header from Dimitar Berbatov to lash home the winner from a tight angle.
Nani had earlier gone close with a firm header from a Gary Neville cross while a bouncing 35-yard effort from Paul Scholes in the first half forced goalkeeper Igor Akinfeev to save.