It could have been a lot worse for Louis van Gaal's side, who are in a healthy position midway through the Champions League group stages.
In addition to the hosts 15th-minute opener, David de Gea had to claw away Ahmed Musa's effort from distance and United initially offered little response with any attacks lacking pace and purpose.
But Marouane Fellaini's introduction at half-time signalled a second half improvement, as Ander Herrera dropped deeper and injected more pace and urgency into the visitors passing.
It was from Herrera's pass that Valencia crossed for Martial to head in his first Champions League goal.
Questions may once again be raised about van Gaal's team choices, with the United boss opting for Martial on the left wing, Wayne Rooney down the middle and 22-year old European debutant Jesse Lingard on the right.
Martial continued in the same position as he did against Everton on Saturday, tasked with keeping an eye on CSKA right-back Mario Fernandes who was a constant threat.
The hosts defenders were quick to surround the former Monaco forward during the first half as he struggled to make an impact in attack.
But the 19-year-old changed the complexion of the match with a brilliant header from 12 yards for his fifth goal of the season.
The strike came from a central position, where the £36m signing has largely played in his early United appearances, and with Rooney failing to make a huge impact in his place, it will be interesting whether van Gaal keeps them there for the derby.
Despite being our top scorer this season with six goals, Rooney spent long periods on the game's periphery.
Playing at the focal point of the visitors attack, he had a half-chance in the first period from Valencia's near post cross, and a second-half header was well saved by CSKA keeper Igor Akinfeev.
The 29-year-old touched the ball only 40 times, more than De Gea's 39 but less than Fellaini's 47 despite the Belgian only coming on at half-time.
Van Gaal has already defended his captain this season but if Rooney is so crucial to our success, it is arguable that he needs to play in a position where he is more involved.