However, City failed to return to the top of the table after Arsenal won 2-0 at home to Fulham, while Cardiff now prop up the top flight as their relegation rivals Crystal Palace beat Stoke 1-0.
Craig Noone stunned the Etihad Stadium just before the half-hour mark when he cancelled out Dzeko’s 10th-minute opener, which brought up the century for 2013/4. But within four minutes, Jesus Navas restored the home side’s advantage.
After the break, man-of-the-match Yaya Toure strode through to score on 76 minutes and substitute Sergio Aguero was also on target shortly afterwards. Cardiff did pull another goal back in stoppage time through Fraizer Campbell but like all the other Premier League visitors to the Etihad so far this season, they went home empty handed.
Manuel Pellegrini made seven changes to his team after the emphatic FA Cup victory over Blackburn in midweek. Dzeko, Navas, Alvaro Negredo and Javi Garcia were the only survivors. Vincent Kompany, Toure and David Silva were all back in action, while Fernandinho and Aguero were substitutes.
Cardiff, for whom recent signing Magnus Wolff Eikrem was again among the substitutes, had Jordon Mutch back from injury among four changes from the home defeat by West Ham. Kevin McNaughton, Ben Turner and Aron Gunnarsson also started. Bo-Kyung Kim, Mark Hudson, Declan John and Peter Odemwingie dropped to the bench.
In the first minute, Dzeko had a shout for a penalty, going down under McNaughton’s challenge after Silva’s ball in from the left. Navas then put the follow up wide.
Cardiff goalkeeper David Marshall had to make smart stops to deny Dzeko and his own defender Ben Turner in the early stages, but the opening goal was to arrive on 14 minutes.
Dzeko had the Goal Decision System to thank as Silva squirmed into the box on the left and pulled the ball back for the Bosnian to strike. It looked like a miskick and McNaughton got back to hoof it out, but GDS showed the ball had already crossed the line.
Having brought up the 100-goal milestone, Negredo twice threatened to extend Man City’s lead – but it was Noone who notched next at the other end.
Assisted by Gunnarsson, the former Plymouth Argyle and Brighton winger came in off the right flank, easily tricked Kompany in the area and coolly scored past Hart just before the half-hour mark.
Normal service was resumed four minutes later. Toure and Dzeko showed great strength in the build-up, and the Bosnian’s shot was blocked – but the ball ran loose to Navas to put the hosts ahead again.
Dzeko had another penalty appeal turned down before the break, after which Mutch and Noone both tested Hart with shots from outside the area.
However, it would be Toure who would score next on 76 minutes. Having appeared to give the ball away to Noone inside his own half, the Ivorian then managed to get it back and strode forward. He played a one-two with Aguero on the edge of the box and then fired home low past Marshall.
A fourth Man City goal duly followed. Toure, near the halfway line, looped a ball into the right channel for Aguero to run onto. The Argentinian tricked Steven Caulker and finished superbly past Marshall for what was the club’s 900th Premier League goal since the competition began in 1992.
In stoppage time, Campbell bundled home a consolation goal for Cardiff when a corner came across the penalty area.
Man City are back in action on Tuesday night when they defend a five-goal lead in the second leg of their Capital One Cup semi-final at West Ham. On Saturday, they host Watford in the FA Cup fourth round, when Cardiff go to Bolton.