Sterling had wasted a excellent chance at that time he shot into the net to give City the lead afterwards 15 minutes, and then he wrapped up the points having a close range finish after the break.
Luka Milivojevic made it an unexpectedly nervy finale to Pep Guardiola’s side if he whipped in a free kick from the edge of this box nine minutes in the conclusion, but Jesus had the last word as he piled a 90th-minute counter-attack.
City travelled a point clear with the triumph, only to collapse back to second once more following Liverpool’s victory over Chelsea.
Sterling has 21 aims for City this season in all contests and Guardiola praised his capability to shrug off events that don’t go his way.
“The Burnley overlook was worse than today,” he told a press conference.
“We have to learn from golfing and other sports such as that — the most essential action is the next one. You overlook, you need to overlook it and go for the next one. He made an unbelievable finish and the pass in Kevin was outstanding. The concluding from Sterling was unbelievable.”
Sterling said he was familiar with the situation and added that City can’t afford any slip-ups in their name race with Liverpool.
“When I was younger you constantly want to evaluate your very first opportunity and at times it does not happen like that,” he explained.
“You do not beat yourself up. There is 80 seconds left, so you merely have to be prepared for another opportunity. That’s the mindset, just keep going and the chance will come.”
City started intentionally, fashioning an early half-chance for David Silva, who was just not able to connect cleanly with a non Kyle Walker cross. They also missed a golden chance following 10 minutes when Silva did brightly to get to the byline and cut the ball back into the devious Sterling, who may only roll it past the pole.
However Sterling made amends about this quarter of the hour mark when Kevin De Bruyne‘s pass down the best allowed him to progress into the area and fire house an angled end.
The home side soon had an accident dilemma, Jeffrey Schlupp limping off following a collision and being replaced by Cheikhou Kouyate, together with City continuing to sabotage and Scott Dann doing nicely to clear the following Silva cross.
Sterling showed the other side of his match, tracking back to help Walker deal with Wilfried Zaha, and Aguero fired around as City maintained their hands.
But Palace revealed a flicker of attacking life soon later, Milivojevic crossing and Christian Benteke moving right \before City hacked obvious.
Shortly after the half-hour, Sane made a good save from Vicente Guaita if he fired an angled drive towards the near post.
Guaita was in the thick of the action again when the ball dropped to De Bruyne and that he fired goalwards, and then Benjamin Mendy‘s strike was directly at the Palace keeper.
But the visitors doubled their advantage after 63 minutes, Sterling again on the mark if he coolly converted Sane’s angled cross from the left.
Dann headed well over in the Palace corner, also City took off Aguero and replaced him with Gabriel Jesus with one eye on next week’s Champions League game against Spurs.
McArthur made way for Bakary Sako for Palace, John Stones replacing Sane for City, who removed some lingering doubts concerning the effect when Jesus kept his cool after De Bruyne had played him into the area.