The victory means it is two wins out of two for Jose Mourinho's side in the 2017/18 UEFA Champions League, leaving them top of Group A.
Mourinho made five changes to his side for the game in Russia, switching to a back three of Victor Lindelof, Eric Bailly and Chris Smalling.
The club's official Twitter account provided the team's starting lineup:
The Red Devils got off to a flying start with Lukaku opening the scoring after just four minutes.
The Belgian began the move, spraying the ball out wide to Martial on the left, who cut inside before crossing for the striker to outmuscle Sergei Ignashevich at the far post and head home.
The goal was Lukaku's ninth of the season in all competitions, and another example of what a superb buy he has been for the club, according to James Robson of the Manchester Evening News:
A second goal followed 15 minutes later, after Mkhitaryan scurried into the area only to be brought down clumsily by Georgi Shchennikov, leaving the referee to point to the spot.
Up stepped Martial to coolly slot home the penalty, sending goalkeeper Igor Akinfeev the wrong way, his bright start to the game impressing football writer Liam Canning:
A good night then took an even better turn as Lukaku scored his second after some poor defending from the hosts.
Again Martial was involved, teasing two defenders before firing in a cross that Vasili Berezutski should have cleared, but his miskick fell to Lukuka to slot home from close range.
It was an emphatic first-half display from United, and the improvement in the team under Mourinho, and the difference in class between the two sides was noted by Goal's Kris Voakes:
The visitors increased their lead after the break, with Mkhitaryan grabbing a goal after more poor defending, Ignashevich's pass easily intercepted by Ander Herrera.
The midfielder gave it to Martial and although his shot was saved by Akinfeev, Mkhitaryan was the quickest to respond, and slotted home the rebound.
Martial then set up substitute Jesse Lingard for a chance that was well-saved by Akinfeev, another example that the Frenchman is playing the best football of his United career, per ESPN FC's Alex Shaw:
The forward was subsequently replaced by Marcus Rashford, with Mourinho seemingly keen to keep his players fresh with his team 4-0 up and the three points effectively secure.
There was some consolation for the hosts, Aleksandr Golovin dinking a ball over the United defence for substitute Konstantin Kuchayev to fire through David De Gea's legs in the 90th minute.
The lack of a clean sheet may not impress Mourinho, particularly with the goal coming so late, but it was a ruthless performance from United with Lukaku and Martial taking full advantage of some generous defending.