Sarr opened the scoring five minutes into the second half, with his shot slipping through the hands of David De Gea at his near post.
The winger was then fouled by Aaron Wan-Bissaka inside the penalty area only two minutes and 45 seconds later to allow Deeney to double the lead from the spot for his first goal of the season.
Ben Foster denied Man Utd substitute Paul Pogba and Marcus Rashford late on as bottom-placed Watford claimed a first home win of the season to move level with Norwich City in 19th on 12 points.
United sit eighth with 25 points after a first defeat in seven matches.
Watford: 26 Dec v Sheff Utd (A)
Man Utd: 26 Dec v Newcastle (H)