United, beaten in their last two away Premier League games and at Basel last week in Europe, began slowly but Young, without a goal for 18 months, struck twice in six minutes midway through the first half before Anthony Martial scored a third before the break to knock the stuffing out of the hosts.
Watford made a fight of it after the break with substitute Troy Deeney scoring from the penalty spot and when Abdoulaye Doucoure grabbed a second in the 84th minute it seemed the hosts could snatch an unlikely point.
Two minutes later, however, Jesse Lingard scored a superb individual goal on the counter-attack to settle United's nerves.
Second-placed United have 32 points with City, who host Southampton on Wednesday, on 37.
"We had chances to make it four, five and six," United manager Jose Mourinho told reporters. "Maybe we thought it was too easy. Maybe it was a good lesson.
"It's good to have lessons without losing points. The next time we are 3-0 up they will remember this.
"But I prefer to forget the five minutes they scored twice and focus on the good things we did because there were many."
Watford, buoyed by successive Premier League wins, were lively in the opening stages and Richarlison was inches away from connecting with a Kiko Femenia cross.
But the game changed in the 19th minute when left back Young beat Herelho Gomes with a powerful shot inside the near post.
Six minutes later United were awarded a free kick in a central position 25 metres out and Young, rather than expected taker Paul Pogba, planted an exquisite curler beyond Gomes.
Things went from bad to worse for Watford as Martial was played in by Romelu Lukaku and the Frenchman found the net with a low right-foot shot.
Richarlison headed against the bar for Watford after the break but they were eventually rewarded when Deeney beat David De Gea from the spot after Marcos Rojo, on his first game back after a long injury lay-off, fouled Roberto Pereyra.
Doucore guided home Andre Carrillo's cross soon after to set up a frantic climax, but Lingard set off on a long solo run, beating two Watford defenders and firing past Gomes to leave United as worthy winners.
(Reporting by Martyn Herman; Editing by Toby Davis)
