Nigerian forward Emmanuel Dennis lobbed a stranded Sergio Romero from 30 yards to give Belgian league leaders Brugge the lead on 15 minutes at a chilly, rainswept Jan Breydelstadion.
Martial though hauled United level before half-time with an excellent run and finish after pouncing on a defensive lapse from Brandon Mechele.
"It was a difficult game against a well-organised team, under difficult conditions. I don't think it was one of the best games anyone has seen," said United boss Ole Gunnar Solskjaer.
"It was a bit sloppy in terms of concentration but conditions with the pitch and ball makes it hard. We got an away goal, we got a draw and we're at home next week. Hopefully we can finish the job."