Scott McTominay scored the winner in the fifth minute with a perfectly placed header from Alex Telles' corner.
Here are the player ratings from Old Trafford.
Dean Henderson 7/10: At times, Henderson looked erratic but between the sticks he had aggression, confidence and kept a clean sheet.
Brandon Williams 7/10: Williams - who had not started a game since United's 3-0 victory away to Brighton in the Carabao Cup - looked sharp and played with a fantastic attitude despite rumours of the defender leaving on loan in this transfer window.
Axel Tuanzebe 7/10: Tuanzebe provided great cover alongside Bailly and Maguire throughout the game. Tuanzebe's best involvement was clearing the ball from Adam Mesina's flicked effort.
Eric Bailly 7/10: Just as the Ivorian defender was putting together a run of form, he suffered an injury late in the first half from his own keeper. Henderson clattered Bailly and it looked as though he went off with a neck injury. Earlier in the game, Bailly got his head to another corner-kick from Telles which narrowly went wide.
Alex Telles 8/10: Telles returned to the starting lineup which presented Luke Shaw the opportunity of a rest. He whipped in consistently dangerous crosses all night - one of which led to the opening goal from a corner, which McTominay got his head on.
Scott McTominay 8/10: It was his first appearance as captain of Man United. The Scottish midfielder put in a true captain's performance as he took charge of the game early and scored the opening goal. His headed goal came from a delightful corner kick taken by Telles.
Donny van de Beek 7/10: It was probably the best performance from Van de Beek in a United shirt, when on the ball he was composed and passed with purpose. He looked smooth and comfortable in his free-roaming role.
Juan Mata 7/10: Mata's elegance on the ball was on show yet again, the Spaniard delivered short and sweet passes to individuals in better places than himself. All that was missing from Mata was an assist.
Jesse Lingard 6/10: For a player who's last start came over three months ago, Lingard provided a spark and sourced creativity from his centre-attacking-midfield role.
Daniel James 7/10: James found great space out wide and ran at defenders determined he was going to get the better of them. James played with a sort of confidence about him, but like other performances he lacked any end product.
Mason Greenwood 5/10: Greenwood acted as the lone striker throughout the majority of the match which United fans had been looking forward to, his natural position. But he found himself playing out wide and running at defenders with no real purpose.
Harry Maguire 7/10: Came on to replace the injured Bailly and continued what he started. Dominant at the back with a commanding tone and presence about him.
Marcus Rashford 6/10: Had a wonderful opportunity to put the game to bed and struck his shot directly at the Watford keeper.
Anthony Martial 5/10: Despite coming on with time to make an impact, Martial did very little and didn't really get on the ball. With Edinson Cavani's ban now over, the Uruguayan striker could be battling Martial for a starting spot vs Burnley and Liverpool.
Nemanja Matic N/A