The Reds have now gone 23 Champions League home games without defeat but it needed two late goals to preserved that record after an indifferent performance for much of the game.
For Moscow this was their first appearance at Old Trafford and they will be bitterly disappointed not to have taken all three points for only the second time on their Champions League travels, and none more so than their keeper Igor Akinev who had kept his team in the game for long periods of the game.
United had dominated the opening twenty minutes of this Champions League Group B tie without ever looking impressive.
Yet, without being at their best United had created enough chances from the wing play of Antonio Valencia to be comfortably ahead.
The visitors, for their part had looked good going forward but only had an effort from Tomas Necid to show for their endeavours.
But the whole nature of the game changed in six minutes.
Against the run of play Moscow took the lead. Necid chested the ball into the path of Alan Dzagoev who raced clear of the Reds defence to hook home from a tight angle.
United responded almost immediately and a Valencia cross was finally converted from close range by Owen.
However, within a minute any thought that the hosts might kick on from this equaliser were quickly dashed.
Again Necid was the provider, this time for Milos Krasic who burst through a static Reds backline to round keeper Edwin van der Sar and stun Old Trafford with a simple finish.
It then got worse for the home side as slack marking at the beginning of the second half allowed Vasilli Berezutski to meet a free kick unmarked at the back post to head past a flat footed van der Sar.
Fletcher was booked for diving when he was clearly fouled inside the penalty area and it seemed as if all the home side's pressure would come to nothing until the final eventful 12 minutes.
Owen and Rooney had efforts blocked until Scholes reduced the deficit with a glancing header from Gary Neville's free kick with seven minutes remaining.
United poured forward and in the first minute of added time Valencia's shot took a wicked deflection off Georgi Schennikov for a leveller that had looked unlikely at the beginning of the half.
There was still time for Moscow's disappointing night to continue with the late dismissal of Deividas Semberas for a second yellow.
United boss Sir Alex Ferguson was delighted with the fightback but tempered with the way his revamped 4-4-2 formation had been exposed.
"We went very open tonight with that formation as I wanted to see how we coped.
"Unfortunately with the players we had we were strung out very easily, but in saying that we had enough chances to be four up before they scored, but at this level if you give the opposition a break you will struggle.
"When they scored that third goal we lost our way a little for twenty minutes but more than deserved the result for we played for the rest of the game.
Ferguson said of the decision not to award a penalty when Fletcher was booked for simulation: "I can't believe it. I can't believe the decision. It's one of the worst I've seen in my lifetime. Why, when you have sidestepped a defender six yards out would you want to dive?"
"I thought the intensity of our play, and particularly in the last 25 minutes, was terrific."