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.
TWEET OF THE MATCH
"Sterling has scored his first goal for Manchester City
Bargain!" - Match of the Day host Gary Lineker.
https://twitter.com/GaryLineker/status/637641979770372096
PLAYER RATINGS
Manchester City
Joe Hart: 6 (out of 10)
Bacary Sagna: 7
Eliaquim Mangala: 7
Vincent Kompany: 7
Aleksandar Kolarov: 7
Yaya Toure: 7
Fernandinho: 8
Jesus Navas: 5
David Silva: 7
Raheem Sterling: 8
Sergio Aguero: 7
Substitutes
Samir Nasri: 6
Fabian Delph: 5
Kelechi Iheanacho: 5
Watford
Heurelho Gomes: 6
Allan Nyom: 6
Sebastian Prodl: 7
Craig Cathcart: 7
Jose Holebas: 6
Etienne Capoue: 6
Valon Behrami: 6
Almen Abdi: 6
Odion Ighalo: 6
Jose Manuel Jurado: 7
Troy Deeney 7
Substitutes
Ikechi Anya: 5
Miguel Layun: 5
Ben Watson: 5
STAR MAN
Raheem Sterling
The former Liverpool star was one the livelier players as City looked for an opening in the first half and had a couple of good chances
He then got the goal his performance deserved, and put City firmly in control of the game, in the second minute of the second half.
MOMENT OF THE MATCH
Fernandinho
The Brazilian midfielder was also impressive and scored a superb goal to put City 2-0 ahead
He won the ball after a Yaya Toure free-kick was blocked and followed up his own hard work to take a return pass from David Silva and fire home.
VIEW FROM THE BENCH
Watford manager Quique Sanchez Flores sent his side out to defend and frustrate City
A point seemed the limit of their ambition and for 45 minutes the plan proved effective
They may gain confidence from how they resisted a side with a formidable attack for a long spell
City boss Manuel Pellegrini had to play a more patient game but with such a powerful squad at his disposal, there was never any need to panic
He will feel highly satisfied heading into the international break.
MOAN OF THE MATCH898
It was good to see Pellegrini put some of his youngsters on the bench in Patrick Roberts, Pablo Maffeo and Kelechi Iheanacho - but it would be nice to see some of them on the field a bit more
They only got one minute between them as Iheanacho came on at the end, even though the game had long seemed in the bag.
WHO'S UP NEXT?
Crystal Palace v Manchester City (Premier League, September 12)
Watford v Swansea (Premier League, September 12)
Source : PA
Source: PA