Balotelli, so often the villain since he swapped the Nerazzurri for City, was the star of the show, opening the scoring on the stroke of half-time after a fine first-half performance.
Dzeko netted a second immediately after the restart and Adam Johnson wrapped things up in injury time, as new signing Sergio Aguero watched on from the sidelines.
The impressive performance allowed City to prepare for next weekend's Community Shield clash with Manchester United in style, and they were rarely in trouble after taking a grip on the game from the off.
David Silva thought he had given them a second-minute lead when he slotted home under Julio Cesar, but the officials deemed that Balotelli's run across the goalkeeper came from an offside position.
Balotelli then headed over, before he and Yaya Toure were denied by Cesar.
City continued to attack and Dzeko converted an Aleksandar Kolarov cross, only to turn and see the flag raised once more - this time incorrectly.
Balotelli would not be denied before the break, though, powering a header into the top corner after Cesar had saved from him at his near post.
Dzeko made it two seconds after the restart, finishing clinically after Silva's smart reverse pass, before Cesar saved again from the same player.
Inter threatened briefly when Joe Hart clawed Wesley Sneijder's deflected free-kick over the crossbar, before City wrapped things up, with Shaun Wright-Phillips forcing his way into the box before squaring for the waiting Johnson.
Manager Roberto Mancini praised Balotelli afterwards, and also confirmed Aguero would start the United game on the bench.
"Mario should play like today, always," he told Sky Sports 2.
"Because he has class, he has everything. If his concentration is in his head, he can play like this.
"This week for Sergio will be recovery. He did the Copa America and finished only two weeks ago. He will be ready to come on the bench next week."
In the day's early game, Celtic hammered an Airtricity League XI 5-0.
Irish strikers Daryl Murphy and Anthony Stokes shared three goals, with Stokes getting a brace and Murphy a penalty, while Gary Hooper also scored twice.