United leave it late to win in Moscow
United returned to Moscow's Luzhniki Stadium for the first time since their victory over Chelsea in the 2008 Champions League final and Valencia's shot from a tight angle four minutes from time secured their third successive win in the competition.
The English champions top the group with nine points and are firmly on course to reach the knockout stages as they bid for a third consecutive appearance in the Champions League final.
"It is not easy away from home," United manager Alex Ferguson told reporters. "We showed maturity and good patience. That's the key for me."
Ferguson said the pitch surface had not been a significant factor in the match.
"As I expected, the artificial turf was not a problem for us," he said. "We adapted quickly to it. I said before the game that if you're a good footballer you concentrate on the ball."
Despite missing several key players including Ryan Giggs and Wayne Rooney through injury, United dominated possession in an entertaining first half which lacked clearcut chances.
Midfielder Paul Scholes tested CSKA keeper Igor Akinfeyev with a long-range effort and United captain Gary Neville's shot sailed just over the bar.
The Russians, without injured Brazilian striker Guilherme and Chile winger Mark Gonzalez, were initially content to soak up the pressure but came alive in the second half.
Alan Dzagoyev put the ball in the net shortly after the interval but his effort was ruled out for offside.
At the other end, Nani's diving header was brilliantly stopped by Akinfeyev on the hour and Valencia hit the crossbar as the home team tired.
But the Ecuadorean made no mistake with his next opportunity, latching on to striker Dimitar Berbatov's header and driving a crisp low shot into the far corner.
CSKA have three points from three matches and their coach Juande Ramos said they were still confident of reaching the knockout stages.
"Obviously, Manchester are the big favourites in our group but the other three teams are pretty even," Ramos said. "I think we can fight with (Wolfsburg and Besiktas) for the other remaining spot."