Raheem Sterling scored either side of half-time to complete a comfortable win for Manchester City at Crystal Palace and keep the Premier League title race well and truly alive.

The England forward prodded him after 15 minutes and then rolled in a second just after the hour mark to take City back to the top of the table for a couple of hours, as they barely got out of second gear at Selhurst Park.

Luka Milivojevic pulled one back for the Eagles with a late free-kick but Gabriel Jesus came off the bench to wrap up the points late on.

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There were two changes for Roy Hodgson’s team from last weekend’s crucial win at Newcastle with Scott Dann replacing the injured James Tomkins at the back and Christian Benteke replacing the dropped Michy Batshuayi up top.

Pep Guardiola meanwhile made wholesale changes from the Champions League defeat to Tottenham in midweek with Walker, Kompany, Mendy, Gundogan, David Silva, Sterling and Aguero coming in for Zinchenko, Danilo, Stones, Foden, Fernandinho, Mahrez and Jesus. It was almost as if he was saving his team for Palace which is not a sentence most Eagles fans are used to hearing.

First sight on goal went to the home team as Milivojevic looked to add to the 11 goals he had already scored this season from distance, although most of those had come from closer than 25-yards out in the shape of the penalty spot. Either way his shot sailed over Ederson’s bar.

Unsurprisingly City saw most of the ball in the opening exchanges and should have opened the scoring when Silva wriggled free of James McArthur on the byline and pulled back for Sterling but he somehow skewed a shot inches wide with the goal gaping.

He made up for that miss 10 minutes later, though, when he raced onto Kevin de Bruyne’s through-ball between Patrick van Aanholt and Dann and cleverly lifted the ball over Vicente Guaita and into the net. City fans – and Fantasy Football managers everywhere – rejoiced. It was the least City deserved after the opening quarter of an hour.

Things went from bad to worse for Palace five minutes later when Jeffrey Schlupp hobbled off down the tunnel having failed to recover from colliding with Vincent Kompany in the lead up to the away team’s goal. He was replaced in the Eagles midfield by Cheikhou Kouyate.

Aguero then sent a shot over the bar from just inside the box while Guaita had to have a strong arm to deny Leroy Sane at his near post as a very serious looking City looked to build on that early lead. They certainly hadn’t come to Selhurst to mess about with the Premier League title race against Liverpool entering the final stretch.

Right on half-time a combination of Guaita, some Palace defenders and a few City forwards stopped De Bruyne’s shot from 12 yards out finding the net. The Belgian was really turning it on in the middle of the park, giving Kouyate, Milivojevic and McArthur the run around at times. Not that the Palace midfield were playing badly, but City had really come to put on a show.

By the time the half-time whistle arrived City had managed 77% possession but in classic Hodgson style Palace were still in the game at 1-0; many other teams would have found themselves more goals behind, but under the 71-year-old the Eagles are always in games and still haven’t lost a league game by more than two goals this season.

By the start of the second half, though, it was more of the same. De Bruyne’s low cross was well gathered by Guaita early on as City picked up where they left off.

It took them just over 15 minutes to double their lead as Sane’s drilled cross found Sterling at the back post and he rolled it into the bottom corner. It was perhaps harsh on Palace after a spirited start to the second half but they just couldn’t get the ball to stick and do anything with it against an impressive City side.

Palace battled on regardless and Benteke did find the target with a half bicycle kick on the side that he didn’t quite catch right, leaving Ederson with a simple take. Scott Dann also headed over from a corner a few minutes later to at least give the home fans something to shout about.

City supporters meanwhile sang a very catchy chant to the tune of “Rotterdam” by The Beautiful South all half, content their team were going back to the top of the league. At least for a couple of hours with Liverpool taking on Chelsea in the day’s later kick-off.

And that, really, should have been that until Milivojevic dragged Palace back into it with a precise free-kick right on the edge of the box after McArthur had been felled. Against the run of play perhaps but it brought Selhurst to life and was the Serbian’s second fourth goal in six games.

City were rattled and Palace decided to go for it for the final 10 minutes, bringing on striker Bakary Sako for midfielder McArthur and pumping balls into City’s box with Benteke the target. One ball found Zaha with his back to goal but he couldn’t spin quickly enough to capitalise on a decent first touch. The noise levels raised considerably inside Selhurst and you could almost feel the whole of Liverpool looking on.

But a mistake from Aaron Wan-Bissaka let in De Bruyne in the final minute and he race clear and fed substitute Gabriel Jesus who had an entirety to pick his spot and did just that inside Guaita’s near post, with a hint of offside. City had ridden the storm and wrapped up the game and an important three points.

Palace stay 13th in the table while City’s attentions turn to Anfield to see if Chelsea can do them a favour and then the Champions League next week with the return quarter-final leg against Tottenham with that unprecedented quadruple still on.