The Bosnia and Herzegovina international netted twice, while goals from Stevan Jovetic and Yaya Toure rounded off the rout at the Etihad - leaving City on the brink of glory.
Having witnessed Liverpool draw 3-3 with Crystal Palace on Monday, City knew a win over Villa would leave its destiny in its own hands heading into the final day of the season.
And the Blues did not waste their opportunity, producing a second-half goal blitz that sees them now with one hand on the trophy as they prepare to host West Ham at the Etihad Stadium on Sunday.
Despite the comfortable scoreline, City was made to work hard in patches against a Villa side which held relegation fears for much of the campaign.
The opening goal only arrived midway through the second half as Dzeko finished off a well-worked team move.
The Bosnia-Herzegovina striker then added a second in the 72nd minute with his 16th Premier League goal of the season before City made it even more comfortable late on.
Stevan Jovetic came off the bench with half an hour to go and made his impact when he passed the ball into the corner for the third, before Yaya Toure - so often the talisman this season - added his own stamp to the scoreline with a fourth in injury time.
Barring a huge swing in goal difference, City now just needs a point against West Ham to secure a second title in three years.
City unsurprisingly made the most of the early running, left back Aleksandar Kolarov - in the side in place of Gael Clichy - forcing Brad Guzan into a near-post save after just five minutes.
Midfielder Toure was then denied by brilliant close-range stop from Guzan seven minutes later before David Silva, starting instead of the injured Sergio Aguero, narrowly missed connecting with a dangerous left-wing cross from Kolarov.
The hosts dominated possession throughout the first half, although Villa was dangerous on the break and could have taken the lead had Andreas Weimann supplied a better finish after racing clear on the counter-attack.
But the best chance of the opening period came in first-half injury time as Samir Nasri turned a James Milner cross wide at the near post from point-blank range.
City's onslaught continued in the second half, Guzan called into action twice in the early stages after the restart.
First, the American kept out Vincent Kompany's acrobatic overhead kick, and then produced an excellent save to prevent Kolarov's curling free kick from finding the top corner.
However, Guzan was finally beaten in the 64th minute as Dzeko slotted home from Pablo Zabaleta's low ball into the box after Silva had fed the Argentinian with a superb pass down the right channel.
Pellegrini's side continued to flood forward in search of the second goal, and it duly arrived eight minutes later as Dzeko tapped in his second on the rebound after Guzan had saved from Nasri.
Weimann went close to setting up a tense finale with a header that cannoned off the underside of the crossbar late on, but City was out of sight soon after.
It added a third when substitute Jovetic converted from a pull back by Toure a minute from time.
The Ivory Coast international then added further gloss to the scoreline himself by surging clear from inside his own half and powering beyond a helpless Guzan to give City sight of the title.