Fernandinho was also on target as City chalked up a club record 10th successive league victory with another empahtic performance at the Etihad Stadium.
The result completed a perfect start to the season for City, who will head into the international break with a record boasting 12 points from four games, 10 goals scored and none conceded.
City had to wait until the second half to break promoted Watford’s resilience, but once Sterling had opened his account the result never seemed in doubt.
Sterling may not be the club’s record signing for much longer, with City apparently closing in on a reported £58million deal for Wolfsburg’s Kevin de Bruyne.
But the £49million man was impressive from the start and City, who would not confirm reports De Bruyne was undergoing a medical as they focused on business on the field, were highly efficient.
They were forced to play a patient game as Watford sat back and focused their efforts on defence.
The Hornets were well organised but limited. Captain Troy Deeney seemed to spend more time fulfilling the duties of a right-back than he did leading the line as City probed in the first half.
But with City having played some exhilarating attacking football in their first three games, little blame could be attached to the visitors. They had their own unbeaten record to protect after making three successive draws on their return to the top flight.
City controlled possession but it was 17 minutes before they had a first serious chance. Aleksandar Kolarov curled his free-kick over after Jesus Navas was fouled.
Sterling was one of City’s livelier players and twice got in on goal but Craig Cathcart blocked his first shot and Heurelho Gomes palmed away his second.
Bacary Sagna also tested Gomes while Sergio Aguero turned and flashed an effort wide.
Manager Pellegrini looked a frustrated man as the half-time whistle blew and he made a change with Samir Nasri replacing the ineffective Navas.
The breakthrough came just two minutes after the restart as Watford lost possession outside the area and Sagna whipped in a superb cross. Sterling timed his run perfectly and turned the ball home unmarked from six yards.
The game began to open up and a second goal followed from a free-kick nine minutes later. Yaya Toure’s set-piece was blocked by the wall but the excellent Fernandinho followed up, heading forward for Silva and then rifling past Gomes after taking a return pass.
Soon after Silva curled a free-kick over and Toure blasted over from a good position.
Watford were a beaten side and could not get back into the game. Sterling left the field to a good ovation when he was substituted in the final minute.