The visitors started poorly and fell at the back of when Emmanuel Dennis lobbed Sergio Romero early in the first half.
United equalised when Martial raced through to beat ex-Liverpool keeper Simon Mignolet one-on-one.
Mignolet tipped a Martial shot onto the post however Odilon Kossounou have won it for Bruges however bent wide.
January signing Odion Ighalo made his 2nd appearance from the bench in as many games in the closing levels however did not honestly have an possibility to exhibit what he could be capable of in a Manchester United shirt.
In the end, the visitors will be the happier of the two sides after securing a probably fundamental away goal in spite of a mostly below-par-performance not helped with the aid of the tough conditions created by persistent heavy rain and a robust wind.
The two sides will meet once more at Old Trafford on 27 February.