United had already secured second spot in the Premier League table ahead of the match, but collected all three points on home soil ahead of the FA Cup final against Chelsea next weekend.
Sergio Romero started between the sticks, while Matteo Darmian and Daley Blind were in for rare starts. It was also a very special afternoon for Michael Carrick as the club captain featured for the last time ahead of his retirement.
As for Watford, head coach Javi Gracia made three changes to the team that started against Newcastle United last weekend, with Heurelho Gomes, Gerard Deulofeu and Richarlison coming in for Orestis Karnezis, Etienne Capoue and Troy Deeney.
The first shot of the match came in the 10th minute when Richarlison tried his luck from a long-range free kick, although the Brazilian's effort was never testing Romero between the sticks.
Marcus Rashford then had United's first attempt two minutes later when he unleashed from distance, with the ball sailing over the Watford crossbar, before Sanchez missed the post from a Juan Mata cross in the 16th minute.
United struggled to get going in the first 30 minutes, but they made the breakthrough in the 34th minute when Rashford tapped a low Mata cross into the back of the net after Carrick had produced a trademark long-range pass.
Watford came close to levelling late in the first period when Richarlison met a cross from the right, but his header was kept out by the diving Romero, who then denied Deulofeu from the resulting corner.
Luke Shaw was the first player off the United bench on the hour, and it might well be the final time that the left-back is seen in a Red Shirts shirt as speculation surrounding his futures gathers pace.
Smart work from Sanchez almost saw the home side double their lead in the 66th minute, but Mata just could not connect on a cross from the Chilean, who was United's biggest threat on the afternoon.
Marcos Rojo almost presented Watford with a golden chance to level 20 minutes from time when Will Hughes blocked a lazy pass from the Argentine, but the offside flag was raised when Gray made a movement towards goal.
Abdoulaye Doucoure was next to have a half-chance for the away side, but the midfielder's header was comfortably gathered by Romero in the 82nd minute of what was a poor match for long spells.
Carrick's moment came in the 85th minute when the Englishman was brought off to a standing ovation, and he will now join Mourinho's coaching staff at Old Trafford.
It was far from a classic in Manchester on Sunday afternoon, but United secured another three points to move onto 81 for the season, while Watford end the campaign down in 14th.
MAN UNITED (4-3-3): Romero; Darmian, Bailly, Rojo, Young (Shaw 60'); Carrick (Pogba 85'), McTominay, Blind (Herrera 77'); Mata, Rashford, Sanchez
WATFORD (4-2-3-1): Gomes; Janmaat, Cathcart, Kabasele (Mariappa 21'), Holebas; Doucoure, Hughes; Deulofeu (Deeney 63'), Pereyra, Richarlison; Gray (Chalobah 73')