The home side needed less than two minutes to take the lead, as Sergio Aguero immediately pressed forward before playing the ball in for Fernandinho to turn it in from close range.
John O'Shea had a chance to equalise for Sunderland just a few minutes later, but the Black Cats' captain headed just wide.
Fernandinho almost grabbed a second when Vito Mannone parried the ball to him from an Aguero strike, but he could only volley over.
The visitors had another chance to level the scores when Fabio Borini beat the offside trap, but hesitated before unleashing a wide shot.
Aguero appealed for a penalty late on after taking a tumble inside the box, but his shouts were waved away by the referee.