A third goal sank the Devils' hopes before the break as Brazil defender Douglas Maicon beat Marco Storari off a Milito assist.
The win was secured in a matter of 15 minutes through an impressive display of offensive power that made Inter fans forget the embarrassing 1-1 home draw against promoted Bari that they had to watch a week earlier.
Milan had produced a good pressing in the first 20 minutes, threatening with a spurt from Frenchman Mathieu Flamini, while Brazilian Ronaldinho misfired off a precious feed from his fast compatriot Pato.
A further threat forced Inter's Brazil goalkeeper Julio Cesar to slap a dangerous cross to prevent Marco Borriello's close-range flick, but Inter gradually improved their game and secured the outcome before the break.
Motta opened the scoring on 29 minutes, stunning Storari with a classy volley off a piercing assist from Milito, who on 36 minutes converted a spot kick after Gattuso floored Samuel Eto'o as he headed for the goal off a long Maicon feed.
Inter'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 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.
Another classic game is set between Roma and Juventus, one of eight games scheduled for Sunday.
Brazil is well known for a lot of things specially the sport they call soccer, and if you plan to visit here in Brazil and you don't have a place to stay, here's the right place for you.
BalasHapusHostels in Camboriu