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.”
Solskjaer made six changes to the side that beat Chelsea on Monday, with Romero handed another start in Europe while Victor Lindelof returned from illness to form a three-man defence alongside Harry Maguire and Luke Shaw. New signing Odion Ighalo again began on the bench.
Brugge coach Philippe Clement, once of Coventry City, handed a European debut to 19-year-old Maxim De Cuyper with captain Ruud Vormer only fit enough to start among the substitutes.
De Cuyper nearly popped up with a goal inside three minutes when Dennis escaped Maguire and skipped towards Romero, his attempt to pull back resulting in Nemanja Matic hooking against the teenager and the ball ricocheting fortuitously over the bar.
Andreas Pereira, United’s Belgium-born Brazilian midfielder, saw a low 20-yard drive tipped behind by Simon Mignolet, with the Brugge goalkeeper setting Dennis up for the opener moments later.
A long kick forward caught United short in defence and Dennis, who scored twice against Real Madrid at the Bernabeu in October, outmuscled Brandon Williams before lofting over Romero with the Argentine well off his line.
An increasingly ragged United were fortunate not to fall further behind when Mats Rits scuffed wide before Romero positioned himself expertly to keep out Dennis from a tough angle.
– Martial takes advantage –
Brugge then paid a heavy price when Mechele allowed a bouncing ball to run beyond him, an alert Martial seizing on the opening to race clear and steer calmly beyond Mignolet.
Martial almost bagged a quickfire second as he smacked the post just before the interval, Mignolet extending a vital hand to divert the Frenchman’s curling strike from just outside the penalty area.
Brugge will be without Eder Balanta for the return leg at Old Trafford next week after he was booked for a foul on Juan Mata, and the Colombian was replaced by Vormer early in the second half.
Jesse Lingard stabbed wide while lunging to reach a teasing ball from Diogo Dalot before Dennis was again denied by Romero from a tricky position.
Odilon Kossounou squandered a superb chance to put Brugge back on top when he scuffed wide following terrific work on the right from Dennis and a clever dummy by Siebe Schrijvers.
Ighalo came on for Martial just past the hour but it was the introduction of Bruno Fernandes for the final 10 minutes that injected fresh life into United. Although the 2017 champions were unable to administer a knockout blow they will fancy their chances of wrapping up the tie on home soil.
Elsewhere, Celtic keeper Fraser Forster saved a late Jens Stage penalty in a 1-1 draw away to FC Copenhagen after Odsonne Edouard’s opener was cancelled by an effort from Senegalese striker Dame N’Doye.
La Liga surprise package Getafe defeated last season’s Champions League semi-finalists Ajax 2-0 in Spain with Brazilian duo Deyverson and Kenedy on target.
Christian Eriksen bagged his first Inter Milan goal in a 2-0 win away to Ludogorets of Bulgaria. Romelu Lukaku added a late second from the spot.
Record five-time winners Sevilla needed an 82nd-minute equaliser from January arrival Youssef En-Nesyri to salvage a 1-1 draw at Romanian outfit Cluj.
Meanwhile, Japanese midfielder Daichi Kamada scored a hat-trick as Eintracht Frankfurt defeated Salzburg 4-1.
