Sterling took the game away from the home side before half-time, firing in a rising shot to open the scoring before doubling the advantage by following up his own saved penalty – awarded for a foul on him by Will Hughes.
Phil Foden added a third after Ben Foster had parried a Sterling shot before Aymeric Laporte nodded in from Kevin de Bruyne’s free-kick.
Sterling has now scored 19 Premier League goals this season, his outright best return in the competition in a single campaign
Watford XI: Foster, Mariappa, Kabasele, Dawson, Femenía, Sarr, Doucouré, Cleverley, Hughes, Pereyra, Deeney
Subs: Gomes, Welbeck, Masina, Chalobah, Cathcart, João Pedro, Gray, Quina, Pussetto
Man City XI: Ederson, Walker, García, Laporte, Cancelo, De Bruyne, Rodri, Bernardo Silva, Foden, Gabriel Jesus, Sterling
Subs: Stones, Gündogan, Zinchenko, Silva, Mendy, Fernandiho, Mahrez, Otamendi, Carson