The tie was effectively over as a contest by the half hour mark through Romelu Lukaku - his ninth and tenth goals of a prolific season - either side of an Anthony Martial penalty.
Konstantin Kuchaev's last-gasp goal proved little more than a consolation for the rampant Reds, who scored four for the fifth time in nine competitive meetings this season.
The win sees United sit top of the standings with two wins from two, after Basel responded from their defeat to us last time out to thrash top seeds Benfica 5-0.
Lukaku began the rout inside five minutes when he powered in a trademark header for his ninth goal in as many games after the outstanding Anthony Martial had picked him out.
David de Gea saved well from Alan Dzagoev as the Army Men threatened an instant riposte, but United were in devastating form going forward and quickly moved further ahead.
Igor Akinfeev denied Henrikh Mkhitaryan, but the excellent Armenian was scythed down by Georgi Schennikov when he challenged for the loose ball.
Martial stepped up and despatched the spot-kick beyond Akinfeev with aplomb for his fifth goal of an impressive campaign.
Aleksandr Golovin flashed a shot wide but United continued to press and put the result beyond doubt three minutes shy of the half hour mark.
Lukaku pounced on Vasili Berezutski's defensive error, from a Martial cross, with the simplest of finishes, as he moved into double figures for the season.
De Gea saved superbly from Fedor Chalov, while Vitinho also went close and the Spaniard was tested again through Dzagoev's speculative strike from distance.
Blind headed over and Lukaku went close to a hat-trick, but Mkhitaryan then got the goal his performance deserved as he made it 4-0 on the rebound 12 minutes into the second half.
Substitute Jesse Lingard was brilliantly kept out by Akinfeev, as the goalkeeper - despite conceding four goals - single handedly prevented an even bigger margin of defeat.
CSKA substitute Kuchaev had the final say with a close-range tap in, but it was only the smallest of blemishes from a very decent night's work in Moscow.
Overall team performance: 9/10
United Faithful Man of the Match: Anthony Martial. Scored one and had a hand in the other three.