Dzeko’s superb solo strike in the first half proved to be enough against a competitive Sunderland side in challenging weather conditions.
After back-to-back defeats in South Africa, City recovered to pick up a semi-final win against South China, before a single-goal victory against Sunderland.
Even though the Black Cats started strongly, Dzeko popped up at the other end with a fabulous finish on eight minutes from 18 yards to hand the Citizens a lead.
Dzeko and new-boy Alvaro Negredo led the attack with the Spanish forward missing a fairly clean effort at goal soon after.
The conditions worsened throughout the half with the heavy rain giving the pitch another soaking.
Most attacks were direct, taking the back-to-front route and Dzeko was denied by Black Cats keeper Vito Mannone on 29 minutes with a low, drilled effort from 20 yards.
The Bosnian turned supplier for Negredo after the half hour mark – but he shot over the crossbar.
Manchester City’s closest attempt at doubling their lead came with seconds to play in the first half.
David Silva’s free-kick was met by Sunderland’s Craig Gardner at the far-post and the ball struck the inside of the post, as the midfielder careered into the other upright.
A frustrating period after the interval was only brought to life by some flashing glimpses from summer signing Jesus Navas on the right wing.
But City fluffed a huge chance to add a second goal on 64 minutes from the penalty spot after a handball from El-Hadji Ba.
Dzeko scored the decisive goal in the semi-final against South China – but he screwed his spot-kick miles over the crossbar which entertained the home fans.
The Bosnian appeared to blame the surface for his error, and he had a point, with the terrible pitch leading Manchester United to cancel an open training session on Sunday.
Navas’ explosive pace was a constant threat on the counter-attack and he was denied by Gardner’s late clearance on the goal-line with 13 minutes to go.
A worrying sight for the City boss was the departure of Matija Nastasic on a stretcher after a sharp turn on the difficult playing surface.
Sunderland struggled to claw their way back into the game with Seb Larsson’s free-kick on 82 minutes forcing a smart save from Pantilimon.
But Manchester City held firm in the mud and torrential rain in Hong Kong, collecting their first piece of silverware this season under Pellegrini.