United looked set to win 1-0 after Dutchman Memphis Depay put them ahead in the 11th minute, a lead they held until Deeney equalised by blasting his penalty past United keeper David De Gea in the 87th after substitute Marcos Rojo brought down Odion Ighalo.
Yet just when Watford appeared to have done enough to secure a point, Deeney diverted a cross from Bastian Schweinsteiger into his own net in stoppage time.
United moved onto 27 points from 13 games, a point ahead of Manchester City and Arsenal and two clear of Leicester City, who are all in action later.
United manager Louis van Gaal, who said on Friday that his compatriot Depay needed to do more to convince him after a disappointing start to his United career, was delighted with the 21-year-old Dutchman's response and his first goal for almost two months.
"He was superb in the first half and this role is the best for him," Van Gaal told BT Sport.
"He played in the same position for me (for the Netherlands) in the World Cup when Arjen Robben or Robin van Persie was injured, and I knew he could do this, but Jesse Lingard was also fantastic and those two created a lot of chances."
United, who are suffering an injury crisis, conceded their first goal in six matches in all competitions.
Van Gaal took heart from their overall performance and the fact they are top "even if it is only for an hour".
"It is a lousy period for us because we have so many injuries, but I hope Wayne Rooney, who is ill and maybe Anthony Martial can come back and play against PSV Eindhoven next week," he added.
Depay broke the deadlock when he connected perfectly with an Ander Herrera cross from the right and volleyed past Heurelho Gomes with his left foot.
Although Watford failed to make much of an impact in the first half, they looked livelier after the break forcing De Gea into some smart saves, although United were also thwarted by Gomes who had a fine match in the Watford goal.
There was a solemn moment before the game when the French national anthem was played as a mark of respect following last week's attacks in Paris, as it will be at matches throughout England this weekend.
(Reporting by Mike Collett; editing by Toby Davis)
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