With two matches remaining on their schedule, City should be prepared and determined to do whatever is necessary to secure two more wins, six more points and the Premier League trophy.
Even if it means making time stop.
So it made sense that if City were going to steal away with the three points they needed to go temporarily back atop the Premier League table, the Sky Blues were going to have to empty their whole trick bag.
Dzeko's first marker came from a midair header. He scored his second standing straight up in Everton goalkeeper Tim Howard's goal mouth.
But Dzeko's most significant contribution to City's win may have come with him face down on the Merseyside pitch.
Dzeko's second goal had given the Citizens a two-goal lead with most of the second half still to play.
For the next 15 minutes or so, very little happened. Everton seemed content to possess the ball without generating much threat, and if they were happy that way, surely City were too.
Once Romelu Lukaku scored for Everton with 25 minutes plus stoppage time left, though, City supporters surely thought that the ghosts of points dropped past were ready to pay another Goodison visit.
City temporarily quelled that possible uprising by pressing Everton back in the aftermath of Lukaku's goal, including a Pablo Zabaleta chance that he really should have buried.
Their initiative, though, left City spread thinner than any club clinging to a skinny lead in enemy territory should ever get. Notably, a City foray into Everton's penalty area in the 79th minute broke down with City players caught upfield.
And that is when Dzeko stood up by falling down.
After losing the ball in a mundane tangle with an Everton defender, Dzeko lay prone on the pitch for about four minutes, and no one knew quite what to do about it.
Referee Lee Probert seemed unimpressed with Dzeko's plight but didn't threaten him with a red card to inspire instantaneous, miraculous healing. That would totally have worked too, since City boss Manuel Pellegrini had already used all of his substitutions.
The trainers eventually came on with the stretcher, at which point Dzeko slowly, gingerly found a way up on his feet, grimacing and clutching his left shoulder.
Dzeko missed about 40 seconds of time with the ball in play.
Everton had chances thereafter, the best coming when Gerard Deulofeu wriggled free in the box to City goalkeeper Joe Hart's immediate left and narrowly missed picking out space at the near post.
On the whole, though, the approximately 14 minutes City and Everton played after Dzeko suddenly felt better were far less menacing and frenetic than were the 80 or so that came before.
Which is the whole point.
How did you feel about Dzeko's dive in the 79th minute?
Especially in the six minutes of second-half stoppage time, City took one of Jose Mourinho's how-to videos on meandering before taking throw-ins and earning corner kicks that then take 30 seconds to launch and made it come to life.
It is a strange thing to watch a side as gifted as Manchester City so definitively and intentionally power down in the seemingly endless closing minutes of a match.
Then again, there is a reason Mourinho wins so many matches 1-0.
If City again manage leads of multiple goals in those upcoming matches, Pellegrini and his charges should continue their recent dalliance in the dark arts.
Time-wasting makes for bad television and sour press conferences, but done correctly, it just plain works.
And there is no room on the Premier League trophy to engrave any aspersions about how the champions won the thing.