Manuel Pellegrini may have a point about festive fixtures. The Manchester City manager is in his first year in England, and simply refuses to accept that playing two games in less than 48 hours is a good idea. He saw his side climb to the top of the Premier League with this victory, for which Yaya Touré, Samir Nasri and Álvaro Negredo were rested, but it was easily City's most unimpressive home win of the season.

After the Boxing Day banquet, this was about as appetising as two-day-old leftovers, and Crystal Palace came close to spoiling City's Christmas by sneaking off with a point. While it might have been imagined that City have reserves of sufficient quality to see off relegation strugglers, that turned out not to be the case. The home side were in danger of spending all day in search of a goal until Pellegrini relented and sent on reinforcements from the substitutes' bench.

"I always knew this game would not be easy," the City manager said. "We were not fresh; it is impossible to play two games in so little time, and it is always difficult when only one team is trying to play.

"The other team just wanted to play for 90 minutes in front of their own goal. I understand why they chose to do that, and sometimes it is very important to know how to win 1-0."

Palace were not quite as negative as that sounds, otherwise Joe Hart would not have been named man of the match for important saves at three crucial moments in the second half, but the pace was slow, the entertainment value low and the crowd restless. The highlights of a stodgy first half came right at its close.

Fernandinho twice came close to scoring at one end, sending a shot over the bar then bringing a save from Julián Speroni with a header from James Milner's cross, while at the other end Palace won a corner to bring a semi-ironic ovation from their travelling support. Apart from Hart taking a boot to the face, the rest of the first 45 minutes was completely forgettable, just a mountain of home possession resulting in a steady trickle of mostly uninspired goal attempts in the Palace half, where almost all the action took place.

Yannick Bolasie did manage a couple of shots for Palace, on the infrequent occasions the visitors ventured across the halfway line, but it was mostly a rearguard action from Tony Pulis's side and, perhaps feeling the effects of their Boxing Day exertions against Liverpool, City were surprisingly short of ideas about how to break it down. A goal was required to open up the game, yet neither side appeared to have enough urgency to create one.

David Silva's attempt five minutes before the interval was typical. Having shown tremendous balance to keep the ball in play on the goal-line and evade Barry Bannan's challenge, he then elected to shoot from a narrow angle when the obvious option was to look up and find a teammate in the middle.

It was as if City thought a goal was bound to arrive eventually, which is probably just what Pulis wanted them to think.

Jason Puncheon possibly showed his hand a little early in bringing a diving save from Hart early in the second half, because after that Pellegrini sent on the cavalry in the form of Negredo and Nasri. He took off two defensive players, kept Edin Dzeko on the pitch and moved Milner to right back, so his intention to win the game could not be doubted.

After Mile Jedinak forced another save from Hart, the strategy worked. Nasri instantly gave City more penetration, and he started the move from which Jesús Navas picked out Dzeko close to the penalty spot with a returned cross from the right. Dzeko crashed the ball home and all Palace's elaborate time-wasting was undone.

"We created some good opportunities and looked quite dangerous on the break," Pulis said. "It's just the final pass or the finish that keeps letting us down. We have done quite well away from home, we just need to turn 1-0 defeats into draws, something that might have happened today but for Joe Hart."

Dzeko almost had another right at the end, again from a cross from the industrious Navas, but his header from a tight angle landed on the roof of the net. A two-goal win would have flattered City: they really were not that good. Whether their present league position flatters City will be shown in the second half of the season. Once they have Touré and Sergio Agüero back, and the benefit of a bit more rest, they should look more like their old selves.