United scored twice in three first-half minutes as Romelu Lukaku diverted Ashley Young's cross in via his chest before Chris Smalling fired home Marouane Fellaini's knock-down.
Watford pulled a goal back midway through the second half through Andre Gray, but despite putting Jose Mourinho's side under heavy pressure for the final 20 minutes, they were unable to find an equaliser.
Nemanja Matic was sent off after a mistimed challenge on Will Hughes saw him pick up his second booking in the closing minutes, but United were able to hold on to claim their 15th victory over Watford in their past 16 meetings.
The result leaves Watford fourth, while United climb to eighth.
The Hornets had the better of the opening 20 minutes, Troy Deeney forcing a superb save from David de Gea, but United grew in confidence immeasurably after their quick-fire double strike.
Lukaku's fourth league goal of the season came in bizarre fashion as he turned home Young's cross with his lower chest.
In contrast, Smalling showed the technique and poise of a seasoned striker to bring down Fellaini's knock-down on his chest and volley into the roof of the net.
However, while Belgium midfielder Fellaini was involved in both goals, it was a Frenchman who was United's heartbeat.
On his 100th appearance for the club, Paul Pogba played with real confidence - testing Foster twice from distance in the first half, before being brilliantly denied on the brink of half-time.
Alexis Sanchez also impressed and did have the ball in the net on 24 minutes, only for his effort to be ruled out for offside, but United were made to work for the win in the second half as Watford grew into the game.
Sanchez and second-half substitute Anthony Martial both had opportunities to make the result safe in late counter-attacks as Watford pressed for an equaliser, but fine interventions by Craig Cathcart and Christian Kabasele denied them.
However, United were not made to pay for those missed chances, as their backline stood firm to close out a hard-earned win and three points.
It was always going to be difficult for Watford to carry the momentum built during their first four matches over the international break, and that proved to be the case.
Despite a promising opening for the hosts, which saw Abdoulaye Doucoure strike at goal after just three minutes, United's first-half goals dampened the Hornets' spirit.
Their central midfield pairing of Doucoure and Etienne Capoue were overrun by United's midfield three in the first half, which left Troy Deeney and Gray starved of service.
But with the game stretched in the second period, Watford were able to get the ball to their creative players more often, meaning the likes of Will Hughes and Roberto Pereyra were able to influence the game.
And it was Doucoure who created Watford's goal, as after a well-worked move he was able to find an unmarked Gray, who applied an emphatic finish to score his second goal of the campaign.
The Hornets then spent much of the remainder of the game camped in United's half, applying relentless pressure, although chances were still hard to come by.
But De Gea kept out another Doucoure long-range effort, and then pulled off a trademark spectacular save from Kabasele's header deep into injury time.
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