In a 234th meeting between the two rivals and a first in Saudi Arabia, it was Inter who made the dream start with the opening goal inside ten minutes.
A brilliant first-time pass from Dzeko released Nicolo Barella in behind the Milan defence, and the Italian midfielder unselfishly laid the ball across the box for Dimarco to power into the net.
Buoyed by the early breakthrough, the Nerazzurri looked full of confidence, and duly doubled their advantage in the 21st minute, when the influential Dzeko cut inside Tonali and fired a clinical strike into the far corner beyond Ciprian Tatarusanu.
In a wide open first half, both sides missed chances before the break - the best of which fell to Martinez, who was inches away from converting an inviting Henrikh Mkhitaryan delivery.
The Rossoneri emerged after the restart eager to gain a foothold in the contest, however wasteful finishing from both Ismael Bennacer and Rafeal Leao only added to their growing frustration.
At the opposite end, Inter continued to look threatening in the final third, but a crucial last-ditch block from Simon Kjaer denied Martinez from pulling the trigger inside the six-yard box.
With 25 minutes left on the clock, Stefano Pioli introduced Charles De Ketelaere and Divock Origi in an attempt to overturn the two-goal deficit.
However, it was Inter who added a decisive third late on, as Martinez held off the challenge of Fikayo Tomori, before clipping a delightful finish over Tatarusanu to seal a historic victory for the dominant Nerazzurri.
Flashscore Man of the Match: Edin Dzeko (Inter Milan)
