United have endured a miserable start to the season, losing two of their first four matches and slipping well off the searing pace set by Liverpool, Chelsea and Watford themselves.
But two goals in three first-half minutes from in-form Romelu Lukaku and Chris Smalling gave them valuable breathing space at half-time and ultimately paved the way to a victory that ended Watford's perfect record.
Rocked by United's strong finish to the first half, Watford pulled a goal back midway through the second period through Andre Gray but failed to find an equaliser.
A relaxed-looking Mourinho singled out Lukaku and Marouane Fellaini for praise. 'I'm very happy with the points,' he said. 'I'm very happy with the spirit, I'm very happy with something that represents for me the spirit of the team -- which is a Lukaku sliding tackle after 50 metres running back to help the team.' The Portuguese manager said he had picked Fellaini to beef up the defence for the past couple of games after costly defensive errors against Brighton and Tottenham.
'I felt that my central defenders, they need especially in this moment of a bit of instability, they need somebody to support them, to give them the first wall, physicality. But Marouane is giving us more than that -- he's giving us that but he's also giving us quality and simplicty.'
Mourinho opted for power rather than guile at Vicarage Road with a physically imposing midfield trio of Paul Pogba, Fellaini and Nemanja Matic.
Former Watford player Ashley Young came in at left-back to replace Luke Shaw, who suffered a head injury while on England duty last week.
Midway through the half Alexis Sanchez had the ball in the net but it was ruled out for offside, and minutes later the Chilean forced a fine save from Watford goalkeeper Ben Foster following a jinking run.
United, backed by their vocal travelling fans, who regularly chanted the name of Mourinho, were establishing a foothold in the game and made their pressure count in the 35th minute.
Watford failed to clear a free-kick and when the ball came back in, Lukaku was on hand to bundle home off his midriff to score his seventh goal as many games for club and country this season.
Foster then kept out a powerful Pogba drive but United were two up in the 38th minute when Smalling controlled a Fellaini header following a corner, and smashed the ball home.
But Javi Gracia's side came right back into the game in the 65th minute when Abdoulaye Doucoure picked out Gray, who arrowed a shot past De Gea.
That goal infused the team and the fans with renewed belief and United suddenly looked shaky as Watford poured forward in search of an equaliser.
There was late drama when Matic was sent off for a second yellow card but De Gea brilliantly kept out a Christian Kabasele header from the resulting free-kick.
Gracia, whose side came into the match on the back of four straight wins, said his team had been outplayed in the first half but had responded well after a team talk.
'I think in the second half we made a step forward and we were able to get out and try to create more chances, with more possession and we competed better,' he said.