Villa held City at bay in a goalless first half, but Sterling scored within a minute of the restart.
In unusually direct style for City, Gabriel Jesus knocked an Ederson clearance forward for Sterling, who took two touches before scoring through Tom Heaton's legs.
It was Sterling's 17th goal in 18 games for City and England this season, coming after a Champions League hat trick against Atalanta on Tuesday, but only his second Premier League goal since August.
Despite desperate defending from Villa, including a goal line clearance by Tyrone Mings, City had added two more by the 70th.
"I think we had some difficulty with a lack of intensity and the rhythm wasn't there but we started the second half really well," City's Kevin De Bruyne said.
A curling cross-shot from De Bruyne eluded everyone and went into the net for 2-0, despite Villa's pleas that Sterling was offside, and a possible touch from David Silva. De Bruyne said "I've no idea" who should be credited with the goal.
Ilkay Gundogan made it 3-0 when Villa failed to clear a corner.
The win sees City retake second place from Leicester, which beat Southampton 9-0 on Friday. City sits three points behind Liverpool, though the league leader can restore a six-point gap with a win Sunday over struggling Tottenham.
With Rodri injured in the Atalanta game, Pep Guardiola started Fernandino and John Stones at center back. Following a muscle injury, it was Stones' first start for City since the 3-2 defeat to Norwich on Sept. 14.
Sergio Aguero was rested after scoring twice against Atalanta.
City's problems deepened with a late sending-off for Fernandinho after a second yellow card. Stones briefly required treatment after being struck by the ball.
"It's part of the game and it's not nice as you want everyone to be there but it's OK," De Bruyne said of City's defensive dilemma, which also includes injuries to Aymeric Laporte and Oleksandr Zinchenko.
But the defense was rarely tested by Villa, whose best chance came when Ederson dived to stop a curling shot from John McGinn in the 22nd minute. Villa appealed for a penalty when Douglas Luiz was tackled in that incident, but it wasn't given following video review.
At the other end, Gabriel Jesus and David Silva missed good chances from close range in the first half before Sterling put City on course for the win early in the second.