Anthony Martial's second half header earned United a deserved point in Moscow to move the Reds up to second in Group B.
Martial had been at fault for Seydou Doumbia's opener for CSKA having given away a penalty, but the young striker nodded in Antonio Valencia's cross to atone for his error and ensure a valuable point for the Reds.
To say United deserved to win is probably stretching things, but we were certainly worthy of a point after an improved second half performance.
In a match relatively short on clear cut chances, Louis van Gaal perhaps had one eye on Sunday's Manchester derby as he rested Juan Mata, Matteo Darmian and handed a European debut to 22 year-old Jesse Lingard.
With every team in Group B on three points you would expect a tight opening to the match, played in near-freezing conditions on a plastic pitch, so it was something of a surprise when the home side took a 15th minute lead.
Having initially saved Mario Fernandes' shot, it turned out the referee had already awarded a spot-kick after Martial had handled the right-back's flick on.
David de Gea pushed Roman Eremenko's on to the post but Doumbia was the fastest player to follow up and sweep home the rebound.
Wayne Rooney's 25-yarder dropped narrowly wide, but United also found themselves 2-0 down at the break when De Gea tipped over Ahmed Musa's dipping drive on the half hour mark.
The pattern of the second half mirrored that of the first, with the Reds knocking the ball around nicely but with very little to show for it.
Rooney got a glimpse of goal just past the hour mark when Ander Herrera whipped the ball in and the United skipper headed goalwards, but CSKA keeper Igor Akinfeev saved well.
The best opening of the match arrived three minutes later when Herrera released Lingard but the young forward snatched at the chance and Akinfeev held on.
A United goal looked imminent and it duly arrived on 65 minutes as Martial pulled the visitors level.
Valencia powered down the right and sent in an excellent cross which was met by a fine header from the French forward which rolled in via a post.
Substitute Marouane Fellaini went close late on after fellow sub Memphis and Martial had linked up well, but that proved to be the last opportunity for us ahead of the return with the Russians on November 3.
Wolfsburg beat PSV 2-0 at home in the other Group B game to go top of the section.
Overall team performance: 6.5/10
United Faithful man of the match: Tough one this, no one really stood out. Valencia was probably the pick of the bunch.