The home side had kept Manchester City at bay for most of the first half but Ben Foster’s goal was finally breached five minutes before the break.
A cross from Algerian Mahrez was edged past the goalkeeper by the chest of Leroy Sane.
Mahrez scored himself shortly after halftime by firing in with his devastating left foot from the middle of the area.
Manchester City were easing to another victory when Abdoulaye Doucoure bundled the ball home after a goal-line scramble five minutes from time to give Pep Guardiola’s side a nervy finish.
Watford, who have not won since October, pressed in vain for an equaliser as they suffered their third successive defeat.
Manchester City, still unbeaten in the league this season, lead the standings with 41 points ahead of Liverpool who visit Burnley on Wednesday looking to keep their own undefeated record intact.
