The Hornets had the best of the chances in an otherwise quiet first half, with Odion Ighalo twice going close to finding the back of the net only to fluff his lines at the last moment.
It was not until the dying stages of the contest that United eventually broke the stalemate, with Juan Mata finding the back of the net with a precise free-kick from 20 yards.
United are now level with fourth-placed Manchester City on points, although the Citizens have a game in hand.
United looked much more potent after Marcus Rashford was shifted to the wing and Anthony Martial moved central. It was the Frenchman who won the foul which led to Mata's match-winning free-kick.
It could have been a different story for the Hornets had Igahlo not been so wasteful in front of goal. The Nigerian has found the back of the net just once in 2016 and continued to struggle on Wednesday night.
Happy to win such a demanding game. All respect to @WatfordFC who fought all the way. pic.twitter.com/qB2IMTZ2C7
— Morgan Schneiderlin (@SchneiderlinMo4) March 2, 2016
A perfect night at Old Trafford @ManUtd#MUFCpic.twitter.com/k0YF2Fn2qc
— Juan Mata García (@juanmata8) March 2, 2016
Manchester United boss Louis van Gaal was pleased with the fight shown by his side:
"I have to give big compliments to our players because when it is physical and you can win at an important moment, when all our competitors are losing, it's very important. We lost against Sunderland and there was a lot of criticism but that is the strength of the league and now you see we are closer to the fourth position so now we are fighting for it."
"We are a little bit disappointed, we try to be happy because the performance was amazing. We played with high personality and we tried to control the match. [United] played well in the last matches, so we prepared well but it was a special moment which decided the match.
*Thanks to Opta
13 - Manchester United have kept more clean sheets than any other Premier League team this season. Drilled.
— OptaJoe (@OptaJoe) March 3, 2016