Pep Guardiola's side started quickly as forward Raheem Sterling opened the scoring on four minutes, nodding home following a cross from Phil Foden. City doubled their lead midway through the first half when midfielder Bernardo Silva struck past goalkeeper Daniel Bachmann.
Silva netted again in the second half -- his sixth Premier League goal in eight games this season -- with a curling shot into the far corner from just inside the 18-yard box.
"There are always things we have to improve but right now, the guys are playing at a really good level," Guardiola said. "We scored three beautiful goals and we could have scored more."
Saturday's result meant City leapfrogged Chelsea, who began the day as league leaders before losing 3-2 away to West Ham, as Guardiola's side sit on 35 points after 15 games. Liverpool are one point behind in second place following a last-minute victory over Wolverhampton Wanderers earlier on Saturday.
Watford, whose boss Claudio Ranieri had previously won eight of his nine career matches against City, are three points clear of the relegation zone in 17th place.