Playing without Paul Pogba, United nevertheless needed just four minutes to find the opener as Romelu Lukaku leaped to head in Anthony Martial's header.
And Martial soon made it 2-0 from the penalty spot after Georgi Schennikov brought down Henrikh Mkhitaryan.
Martial and Lukaku linked up again in the 27th minute, the Belgian tapping home after defender Vasili Berezutski failed to deal with Martial's hopeful ball into the box.
Henrikh Mkhitaryan got in on the fun in the 57th minute by running onto a rebound after Igor Akinfeev had done well to save Martial's shot.
With the game well out of reach, Konstantin Kuchaev added a meaningless goal in the 90th minute for the hosts.