Ole Gunnar Solskjaer's men were made to fight until the very last minute after Watford scored late on, after Rashford and Martial had put the Reds into a 2-0 lead.
Somewhat against the run of play, Rashford had found the net on 28 minutes after a lovely ball from Luke Shaw.
Martial doubled the advantage with 18 minutes left on the clock, before Abdoulaye Doucoure made it a nervy last three minutes of injury time after he pulled a goal back late on.
The result moved United back up to fourth and level on points with Tottenham Hotspur in third.