With United cruising at 3-0 up, Watford struck twice in the closing stages through Troy Deeney and Abdoulaye Doucoure to trim the lead to a single goal before Jesse Lingard's 60 metre solo run four minutes from time settled United's nerves.
Unted boss Jose Mourinho complained his side had squandered the chance to coast to victory.
"In the second-half it should have been 5-0 or 6-0, it was easier to score than the first. It was an easy match to win comfortably.
"But at 3-2 the game is in the balance then Jesse Lingard had the initiative to kill the game."
Manchester City can restore their eight point advantage on Wednesday night with pep Guardiola's men hosting Southampton at the Etihad Stadium.
"Both Lindgard and Ashley Young scored great goals," added Mourinho. "We missed the chance to go 4-0 up with some actions and Romelu Lukaku had an open goal, Paul Pogba had a free header too ... We should be smoking cigars but then were in trouble."
In other Premier League action, last season's runners-up Tottenham Hotspur fell further off the pace with a 2-1 defeat at Leicester City. Jamie Vardy and Riyad Mahrez scored for the hosts in the first-half before Harry Kane halved the deficit with 11 minutes remaining.
Spurs will be 16 points adrift of the pacesetters should Manchester City claim all three points against Southampton.
"Our performance was a clear example of a lack of fight in the first half when we were 2-0 down," said Spurs manager Mauricco Pochettino.
"I think in football first of all you must compete, fight and be focused and then of course the quality will come through."
He added: "Leicester showed more fight than us and were ready to fight. It was difficult to analyse the game because we started so sloppily.
"We need to learn from this game. We need to compete -- if you do not fight in the Premier League then the gap is even. We can't afford to not compete and not fight and expect to win games."