Goals in each half from Marcus Rashford and Anthony Martial got the Red Devils back to winning ways after losses to Arsenal and Wolverhampton Wanderers in the Premier League and FA Cup respectively, despite Abdoulaye Doucoure's late strike.
It was a mostly uninspiring performance from United at Old Trafford, but the result moves it back into the top four at the end of a week in which Solskjaer was confirmed as the club's next full-time boss on a three-year deal.
Doucoure dragged a shot wide from inside the United box as the home side endured a strangely sluggish start in the Manchester sun, but it took the lead 28 minutes in, with Rashford clipping a clever finish over Ben Foster after Luke Shaw won back the ball on the edge of his own area and sent his England team-mate through on goal.
Foster made a smart save with his legs to deny Martial before half-time, as United began to dictate proceedings thanks largely to Solskjaer's decision to shift Juan Mata from the right wing into a number 10 role.
Watford was the better side after the break once more, with David de Gea saving well from Roberto Pereyra and Will Hughes curling a shot wide after Nemanja Matic lost the ball in his own area.
Martial struck 18 minutes from time, scooping the ball into the net after he reacted quickest following a tangle with goalkeeper Foster, and it proved just enough for the victory despite Doucoure slotting past De Gea after a clever link-up with Isaac Success and Troy Deeney.
The win lifts United back into fourth place in the table, a point above the Gunners, who play Newcastle United on Tuesday (AEDT), and level with Tottenham Hotspur in third.
Watford dropped to ninth, but its focus is already on next weekend's FA Cup semi-final with Wolves at Wembley.
United itself heads to Wolves on Wednesday (AEDT), while Watford hosts struggling Fulham.