Motta opened the scoring in the 29th minute, stunning Storari with a classy volley off a piercing assist from Milito, who in the 36th minute converted a spot kick after Gattuso floored Samuel Eto'o as he headed for the goal off a long Maicon feed.
Inter Milan's win was virtually secured 10 minutes later with the dismissal of Gattuso, who received a second yellow card for downing Dutch newcomer Wesley Sneijder.
With AC Milan on the ropes, Brazil defender Lucio had a tight-angle shot blocked by Storari before Maicon's third goal off yet another great assist from Milito.
There was little thrill in a second half that saw Inter control the game and beef up their tally through a smashing long-range shot drilled by Serb Dejan Stankovic in the top right corner.
Earlier Saturday, promoted Bari drew 0-0 at home to Bologna, a week after the far more prestigious draw they snatched at Inter in the season opener.