City have put breathing space between themselves and Liverpool - who play on Sunday - while Watford remain in eighth position and trail Wolverhampton Wanderers on goal difference.
Watford boss Javi Gracia made as many as seven changes for the game in the North-West, but the Hornets did an effective job in frustrating City during the opening 45 minutes.
David Silva diverted the ball wide of the far post from an inswinging cross during the early stages, but it took until the 29th minute for City to really put Watford under pressure.
The resulting corner was only cleared into the path of Riyad Mahrez, who sent a half-volley fizzing narrowly wide of Foster's right-hand post.
Watford would have been delighted having reached the break on level terms, but all of the Hornets' hard work was undone within seconds of the restart as City went ahead in controversial circumstances.
Aguero diverted the ball into the path of Sterling - who was in an offside position - but Janmaat kicked the ball against the winger's shin and the ball looped over Foster and into the net.
The goal was initially ruled out by the assistant, but the referee opted to overule the decision after a lengthy discussion on the touchline.
Gracia was visibly furious and the Spaniard's mood got no better, with Sterling netting his second when getting on the end of low pass across from box from Mahrez.
Sterling's treble was complete by the hour mark, with the winger latching onto a pass from David Silva and dinking a shot over Foster having cut inside two defenders.
The game appeared to be over and Pep Guardiola opted to withdraw his hat-trick hero, but Gracia also decided to make alterations and it led to his side reducing the deficit.
Watford continued to go in search of a second without forcing Ederson into a save, and City soon began to reassert their dominance at the other end of the pitch.
Aguero fired straight at Foster from an acute angle, Bernardo Silva saw an effort blocked by Foster and Sane fired harmlessly wide of the near post from close range.
Nicolas Otamendi also headed wide of the far post as Watford struggled to contain a team desperate to improve their goal difference, but City were left to settle for three goals and three points as they took another step towards retaining their league crown.
MANCHESTER CITY (4-3-3): Ederson; Walker, Kompany, Otamendi, Zinchenko; Bernardo Silva, Gundogan, David Silva; Mahrez (Foden 90'), Aguero (Gabriel Jesus 80'), Sterling (Sane 64')
WATFORD (4-4-2): Foster; Janmaat, Britos (Cathcart 82'), Kabasele, Mesina; Feminia (Deulofeu 66'), Capoue, Doucoure, Cleverley; Gray, Success (Deeney 66')
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