Dzeko broke an 11-match scoring drought at the DW Stadium to send City clear of city rivals United. The giant Bosnian netted his 14th club goal of the season as he headed David Silva's free-kick into the far corner.
It was enough to overcome a spirited Wigan side, although the visitors did have chances to make life a little more comfortable against the basement boys, with Dzeko taking the best chance off the toe of Sergio Aguero.
And Blues boss Roberto Mancini ended the game in animated conversation with the fourth official after Martin Atkinson's inexplicable failure to show Maynor Figueroa a red card for deliberate handball on halfway as he denied Aguero a clear run on goal two minutes from time.
Wigan's adherence to the passing game is very laudable but there are times when their supporters would were prefer a bit of old-fashioned English-style long ball.
Although the Latics were back-pedalling for most of the half, there were enough occasions when they did work themselves into decent positions yet failed to deliver a cross or a pass that might have put their opponents under pressure, leaving their supporters distinctly agitated.
As it turned out, James McArthur had their best chance, a snap-shot from the edge of the area, which Joe Hart gathered at the second attempt.
Silva returned to the City side for Monday's match.
The diminutive Spain international is behind so much of the Blues' most inventive play and with Yaya Toure amongst the five senior figures missing and Samir Nasri struggling for top form, there was more reliance on him than usual.
Silva had a couple of shots blocked, almost sent Aguero through and supplied the free-kick for Dzeko's goal.
Having not found the net since November 5, the Bosnian was in need of one of those fireworks Mario Balotelli had set off in his house.
To that end, he could not have wished for more accommodating opponents.
Wigan failed to get close enough to Dzeko and as Gary Caldwell and Antolin Alcaraz floundered, Dzeko found the corner with a precise header.
Aguero brought a fine one-handed save out of Ali Al Habsi as the opening period drew to a close and, despite the closeness of the scoreline, the suspicion remained that City would cruise clear after the restart.
Yet Wigan remained spirited opposition and with plenty of team-mates in support, McArthur could have picked a better option than a long-range shot from an acute angle that fizzed disappointingly wide.
It was not long before City were back on the offensive, although how they had not increased their advantage by the hour mark was a bit of a mystery.
First of all, Al Habsi made a magnificent double save to deny Dzeko and Silva, clawing the Bosnian's curling effort away from the top corner, then repelling the midfielder, who had aimed low from barely seven yards.
What followed next was infuriating for Aguero, who weaved his way past three Wigan defenders and seemed to have the simplest of tasks to find the net.
Instead, Dzeko whipped the ball off his toe and went for goal himself. But his shot was so weak Al Habsi was able to make a comfortable save.
It meant Roberto Martinez was able to introduce Ben Watson and Franco Di Santo midway through the second period still harbouring hopes of snatching something from the game.
And how close they came too as Hugo Rodallega rolled a pass to James McCarthy on his left and the midfielder forced Hart into his best save of the match.
It was not turning into the cruise many had predicted and the jitters even seemed to get to the normally unflappable Hart, who made a save he did not need to as McCarthy's shot was flying wide.
The introduction of Nigel de Jong for Nasri and Nedum Onuoha for Silva were further signs of City entering preservation mode.
Wigan continued to be the architects of their own downfall though, gifting a chance to Dzeko, which Al Habsi turned away, then costing themselves a decent attacking chance when Caldwell rolled a two-yard pass to Stam straight out of play.
And, though they worked hard to fashion another opportunity, Wigan could not find a talking point to match Figueroa's deliberate handball as he got the bounce of a De Jong clearance all wrong and, knowing he was the last man, stuck up a hand to prevent Aguero bursting clear on halfway.