The Red Devils cruised to a first-half lead at Vicarage Road thanks to an Ashley Young brace and Anthony Martial strike.
There seemed no hope of a Watford comeback until midfield maestro Matic was forced off through injury.
Ander Herrera came on to replace the Serb on the 56th minute but then United began to collapse.
Troy Deeney and Abdoulaye Doucoure pulled the deficit back to one goal as Mourinho’s side were shell-shocked.
But Jesse Lingard eased the nerves with a fourth, four minutes from time.
The moment Matic withdrew was a key component of the game turning, and United fans will undoubtably be worried about his fitness.
And Mourinho has echoed those fears by confirming that Matic has suffered a muscular problem.
“We lost stability when Nemanja Matic had to come out but the important thing is the three points,” Mourinho said.
“I saw happiness from the team and played with a free mind.
“For Matic to tell me he wants to be replaced, he does not do that if it is nothing important. It is muscular.”
United moved to within five points of Premier League leaders Manchester City with victory, although they have a game in hand against Southampton tomorrow (8pm).