Sterling took his goal tally for the season to 21 and Gabriel Jesus chipped in with the third as dominant City passed the latest test of their title credentials.
Selhurst Park has been a graveyard for title campaigns in the recent past, notably when Liverpool’s wheels came off in 2014 and City suffered a similar fate a year later.
Palace were also looking to complete an unlikely double over the champions, as the only visiting team to win at the Etihad this season thanks to Andros Townsend’s wonder-goal.
But with Christian Benteke, handed a first start since February 9, cutting an isolated figure in attack the Eagles failed to lay a glove on Pep Guardiola’s side until Luka Milivojevic scored with a free-kick.
It did not knock City out of their stride, though, with substitute Jesus ensuring they recorded a ninth successive Premier League victory.
City arrived in south London with their Champions League first-leg defeat at Tottenham still fresh in their minds and were without midfielder Fernandinho due to a minor knock.
Sterling should have fired them ahead early on only to sidefoot wide from six yards out after David Silva had cut the ball back from the byline.
But the England forward made no mistake when presented with his next opportunity, in the 15th minute, after Kevin De Bruyne’s through-ball dissected the Palace defence.
Sterling raced between Patrick Van Aanholt and Scott Dann before thumping the ball past Vicente Guaita and into the roof of the net.
The only surprise was that by half-time City had not added to their lead, such was their supremacy as they strolled around in the spring sunshine, with Silva pulling the strings.
Sergio Aguero drove over and Guaita saved well at his near post to deny Leroy Sane before Ilkay Gundogan’s lofted ball into the box had Silva, Sterling and Sane lining up to apply the finish.
Unfortunately, they all rather got in each other’s way and when the ball eventually dropped for De Bruyne his shot was blocked by a wall of defenders.
After the break, Guaita saved at the feet of Sane and Gundogan fired over before Sterling popped up with the second.
Aguero and Silva combined to feed Sane, who drilled the ball first time into the centre where Sterling placed it into the corner.
But as Palace hunted an equaliser they were caught out on the break and De Bruyne fed Jesus in the last minute to wrap up another City victory.