A rather uneventful first 45 minutes was brought to life after the break when Martial's first Premier League goal in six matches gave United the lead.
But Joe Allen capitalised on an error from the Red Devils defence to equalise with little under ten minutes to go.
Martial and Wayne Rooney were brought on midway through the second half and within two minutes of entering the fray the two combined to get United up and running, albeit Rooney's involvement was via an interception that fell into Martial's path.
But there was no doubt once the 20-year-old picked up the ball inside the box before unleashing a perfectly placed shot into the top right hand corner.
United had dominated possession, and the majority of chances, but a lapse in concentration at the back on 83 minutes allowed Allen to capitalise on a rebound off the crossbar before tapping into the empty net and levelling the match 1-1.
Paul Pogba should have won it for Old Trafford club late on when Marcus Rashford picked out the Frenchman unmarked in the box but he somehow crashed his header against the woodwork from just a few yards out.
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Jose Mourinho
"This is the best performance all season and could have been one of these fat results in the Premier League, it could have been 5-0 or 6-0. We had big chances, with amazing saves and big misses.
"We chased the second goal and they go at the other end and score the goal and get a point. You can have sometimes have draws where what you does nothing to change the result.
"The players and I did everything. I made changes, everyone was giving more and more but today we could be here all day without winning the game. We will play worse and win games for sure."