Edin Dzeko's second-half goal proved to be enough to end Palace's resistance and maintain City's perfect record at home as they made it 10 wins out of 10 in the Premier League at the Etihad.
Palace frustrated City for long periods of the game and went close to scoring on a couple of occasions with Jason Puncheon and Joel Ward both being denied by fine saves from Joe Hart.
City fashioned their first chance of the game after just five minutes when David Silva slipped Dzeko in on goal with a brilliant defence-splitting pass, but the big striker dragged his shot wide of the target.
Silva had the next sight of goal for City on ten minutes when Fernandinho teed up the Spaniard on the edge of the box and he fizzed his shot just wide of goal.
Yannick Bolasie had Palace's first effort of the contest five minutes later when he cut in from the left and fired in a shot which failed to trouble Hart.
Palace were defending well and restricting City to efforts from long range, with James Milner firing one over the top before Vincent Kompany saw his deflected effort well collected by Julian Speroni.
Just before the half-hour mark, Hart dived bravely at the feet of Cameron Jerome to stop the striker getting on the end of Jonathan Parr's inviting cross, but it came at a cost to both players.
Jerome was forced off with a knee injury to be replaced by Marouane Chamakh, while Hart suffered a bad cut to his eye.
City continued to push forward in search of a breakthrough and Fernandinho created a chance for himself out of nothing when he skilfully flicked the ball over Adrian Mariappa on the edge of the box only to blaze his left-footed volley over the crossbar.
Deep into first-half injury-time, City forced Speroni into his first serious save of the game when Milner picked out Fernandinho inside the box and the Brazilian saw his header tipped over the top at full stretch.
Palace went close to breaking the deadlock five minutes after the break when Puncheon skipped round the challenges of Gael Clichy and Javi Garcia, and fired in a shot from 25 yards which Hart was forced to turn behind for a corner.
From the resulting corner Chamakh wasted a great chance to give Palace the lead when he headed over unmarked from eight yards out.
Palace were growing more and more confident the longer the game went on and Puncheon was unlucky not to score on 63 minutes with a superb curling effort from the edge of box which flew just wide of the far post with Hart well beaten.
A minute later Mile Jedinak tried his luck from long range with his powerful strike forcing Hart to tip his effort over the crossbar.
City finally broke the deadlock and eased the nerves of the home fans on 66 minutes when Jesus Navas picked out Dzeko inside the box and he drilled his shot high into the net past Speroni.
Palace refused to lie down and were unlucky not to draw level less than a minute later when Ward let fly with a dipping shot from 30 yards which Hart brilliantly pushed round the post at full stretch.
From the corner Ward should have done better when he found himself unmarked at the far post, but the defender could only head his effort into the ground and wide of the target.
Dzeko went close to making the game safe in the closing moments when he got on the end of Navas' cross at the far post, but on the stretch he was unable to direct his effort on target.