Man United boss Jose Mourinho made five changes to the team that started Saturday's Premier League clash with Southampton. Victor Lindelof, Ander Herrera, Chris Smalling, Daley Blind and Martial all came into the XI, with Antonio Valencia, Phil Jones, Marouane Fellaini, Juan Mata and Marcus Rashford dropping out.
As for the home side, key defender Mario Fernandes was passed fit to start following a concussion, while the highly-rated Vitinho and teenage Russian forward Fyodor Chalov started in the final third. There was also a spot at centre-back for 38-year-old Sergei Ignashevich, who is currently in his 14th season with CSKA.
Man United had a lot of the ball in the early moments, and the Red Devils took the lead inside the first four minutes when Martial's brilliant cross was headed home by Lukaku, who had risen above Ignashevich at the far post.
Mkhitaryan had a wonderful chance to double Man United's lead in the 13th minute after meeting a low cross from Blind, but CSKA goalkeeper Igor Akinfeev used his feet to keep out the Armenian's effort.
The visitors had their second of the night in the 19th minute, however, when Martial found the bottom corner from the penalty spot after Georgi Schennikov had brought Mkhitaryan to the ground with a clumsy challenge.
Aleksandr Golovkin fired one just wide of De Gea's post in the 22nd minute as CSKA looked to hit back, but the Russian side continued to struggle down the other end, and Man United scored their third in the 27th minute through Lukaku, who moved into double figures for the season.
Again the goal came from a Martial cross, and after CSKA centre-back Vasili Berezutski had a fresh-air shot at the near post, Lukaku was on hand to tap home at the far post as the Red Devils raced into a 3-0 lead.
Lukaku forced a smart save from Akinfeev 10 minutes before the break as the Belgian looked for a first-half treble, before De Gea had to keep out a decent effort from Chalov down the other end.
Mourinho's side could have scored five or six in what was a rampant first-half performance, but the half-time interval arrived at 3-0 as CSKA were given the chance to gather their thoughts after a difficult opening 45 minutes.
Golovin had the first half-chance of the first period after working some space inside the Man United box, but the attacker saw his effort curl wide of De Gea's post, before Akinfeev kept out a powerful Lukaku strike down the other end after Martial had found the Belgian once again.
Blind was next to come close for Mourinho's side after meeting another excellent cross from Young, but the Netherlands international saw his header miss the crossbar.
Man United had their fourth of the night in the 58th minute, however, when Mkhitaryan found the back of the net from close range after Akinfeev had palmed a Martial strike into the path of the Armenian.
Jesse Lingard almost added a fifth 15 seconds after entering the field, but the England international, who had collected a brilliant pass from Martial, could not find a route past Akinfeev.
Matteo Darmian and Rashford followed Lingard off the Man United bench for the final 20 minutes, and the former had a super chance to score in the 80th minute after being released by Matic, but the Italian could not beat Akinfeev from close range.
CSKA got their name on the scoresheet in the 90th minute when Konstantin Kuchaev found the back of the net from a narrow angle, but it was no more than a consolation on a tough night for the home side.
Man United will now switch their attention back to the Premier League as they prepare to host basement side Crystal Palace on Saturday afternoon, while CSKA are next in league action at home to Ufa on Sunday.