Zlatan Ibrahimovic twice went close to equalising for Milan but the hosts were then caught out chasing the game.
A fine team move saw Martinez tap in his second then Romelu Lukaku finished another incisive counter attack with a low drive into the bottom corner.
⚽️ Watch All Goals and Highlights: AC Milan 0-3 Inter
While the normal raucous atmosphere that usually greets this fixture will have to wait until fans return to stadiums, supporters of both clubs lined the route to the ground, underlining the significance of the match.