England international Sterling opened the scoring with a superb solo goal before setting up Gabriel Jesus to double City's advantage.
Ryan Ledson's own goal before half-time ultimately decided the match.
Speaking after the game, manager Pep Guardiola told Sky Sports: "We made a good solid performance against a team third in the Championship, we played really good.
"I am pleased a lot with Eric Garcia and Taylor Harwood-Bellis at the back, they helped us a lot. They combined, they suit each other perfectly and they have played in the academy every weekend. They are exceptional human beings with a ood mentality.
"I am very pleased."