And following their victory over Aston Villa on Boxing Day, Saturday's performance will certainly give the Eagles further confidence with a vital home game at Selhurst Park against Norwich to come on New Year's Day.
Ward's efforts immediately after Dzeko's goal showed that Pulis has instilled a steely side to his team, though they were perhaps fortunate that City only found the target twice in a first half where they registered 15 shots.
With this encounter coming less than 48 hours after the 2-1 victory over Liverpool on Boxing Day, manager Pellegrini made six changes to the side but Fernandinho and David Silva - who both played in that game - had the biggest impact before the break.
Dzeko's goal means that City have now broken their own Premier League record by scoring 54 goals in 19 games.
City have now also scored in 60 consecutive home league games
Those alterations included a first City league start for Dedryck Boyata since May 2011, while Dzeko replaced Alvaro Negredo in attack.
The Eagles did threaten down the left through Yannick Bolasie but the biggest worry for the hosts came when Hart suffered a nasty cut just below his left eye after a collision with Cameron Jerome.
Hart received treatment on the pitch and was fit enough to continue but Palace striker Jerome was forced off with what appeared to be a knee injury.
Hart reappeared for the second half with his injury clear to see but he remained alert to palm Puncheon's shot wide with substitute Marouane Chamakh heading over from the resultant corner.
Manchester City 1-0 Crystal Palace: Tony Pulis praises 'fantastic' Palace
That scare, along with frustration from the home supporters, prompted Pellegrini to go on the attack and he brought on Negredo and Samir Nasri for Fernandinho and Boyata.
But City were less fluid in the second period and Palace grew in confidence with Puncheon curling wide before Hart tipped Jedinak's long-range effort over the bar.
However, Dzeko appeared to settle City nerves when he tucked in Navas's cut-back but Palace continued to threaten and almost equalised through Ward.
The Eagles midfielder saw his first effort tipped away for a corner by Hart, who flung himself to his left, and his header from the resulting corner missed the target.
That proved to be the last meaningful effort from Palace and after Dzeko almost grabbed a second, his side held on for a fourth consecutive league victory.
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