The Bosnia & Herzegovina striker steered home Jesus Navas’ cut-back midway through the second period to give City their 10th successive victory at the Etihad Stadium.
Yet, after magical performances earlier in the campaign, this fell into the ‘win ugly’ category.
Palace worked with an impressive intensity throughout and City were indebted to superb saves from Joe Hart to deny Jason Puncheon and Joel Ward either side of Dzeko’s 10th of the season in all competitions, but his first in the Premier League for eight weeks.
On statistics alone, Palace might as well not have bothered turning up.
The Eagles had not beaten City away from home since 1990 and their manager, Tony Pulis, had lost on all five of his visits to the stadium, not even managing so much as a goal.
In addition, there was the Blues’ incredible sequence of results on home soil.
The Boxing Day win over Liverpool had been their ninth win in nine, a sequence that had yielded an incredible 37 goals.
Yet despite this gloomy backdrop, Palace still managed to become only the second team since Hull on August 31 to prevent City from establishing superiority by half-time.
There was no secret. The visitors owed their mini-triumph to good, old-fashioned graft and a little bit of luck.
Filling their own box any time City got close – which was fairly frequently – they managed to keep chances at a minimum.
James Milner flashed a couple of efforts narrowly wide and David Silva was not far away from finding the net from an impossibly acute angle.
However, it was not until Fernandinho ventured forward late in that opening period that Julian Speroni’s goal came under severe threat.
The Brazilian lashed a shot over after a brilliant piece of skill had created the opportunity.
He then saw his powerful header touched over by Speroni before having another effort blocked amid a melee inside the Palace area during which Dzeko had spurned a clear sight on goal by preferring to check inside onto his right foot.
It was not exactly comfortable for the visitors, but then Pulis can hardly have anticipated a smooth ride for his team.
Yet they were sufficiently confident to push forward themselves when the chance arose, and Yannick Bolasie ensured Dedryck Boyata was kept on his toes as the City man started a league game for the Blues for the first time since May 2011.
Nevertheless, Hart did not have a shot to save. The England keeper still picked up a nasty gash under his eye though as a result of a full-bloodied challenge with Cameron Jerome that saw the Palace forward hobble off.
Hart was called into action straight after the restart though as Puncheon unleashed a fierce shot from 25 yards, which the keeper turned behind in impressive fashion.
Substitute Marouane Chamakh was not too far away from turning the corner home from his near post station and Manuel Pellegrini wasted little time in introducing Samir Nasri and Alvaro Negredo.
Palace’s confidence was growing though and Hart was little more than a spectator as Puncheon curled a shot that would not have been kept out had it been slightly more accurate.
Such was the verve with which Palace had started the second-half that Dzeko’s goal came as something of a surprise.
Damien Delaney thought he had cleared the immediate danger when he got his head to Silva’s teasing cross.
But Jesus Navas hunted the ball down to the by-line, then picked out Dzeko with a superb cut-back that invited the first-time finish from the Bosnian.
Palace responded admirably. Ward’s dipping volley was heading for the bottom corner until Hart got a fingertip to it.
Ward then got his head on the far post corner, but from close range failed to keep the attempt on target.
Pellegrini’s decision to shelve the intention to introduce Yaya Toure and instead bring on the more defensive Aleksander Kolarov said it all as City scrambled to victory.