The game on the artificial playing surface in the Luzhniki Stadium got off to a slow start, with neither side willing to commit men forward.
It took 26 minutes for the first effort on target to arrive. Paul Scholes struck a stinging drive from 35 yards and keeper Igor Akinfeev bundled the effort away for a corner.
Soon after Tomas Necid threatened from a ball in from the CSKA left, but there was little power in his header and Edwin van der Sar collected with ease.
Ten minutes before the break Milos Krasic beat a couple of United players on the right and shot goalwards, but his effort drifted harmlessly past van der Sar's far post.
Five minutes later Gary Neville came closest to breaking the deadlock, curling a left-footer inches over the top from just outside the area.
The second half started in much the same fashion as the first had, although United eventually managed to gain the upper hand.
They almost broke the deadlock on the hour mark as Akinfeev got down superbly to push away Nani's downward header from a Neville cross from the right.
Eight minutes from time United went even closer, as Nani and Valencia combined superbly in the centre of the pitch and the latter crashed a right-foot shot against the crossbar from 20 yards, with Akinfeev stranded.
Four minutes later United struck the decisive blow as Nani's cross from the left was touched on by Dimitar Berbatov and Valencia crashed the ball home from close range at the far post.