Inter were short of ideas in last weekend's opening 1-1 draw with Bari but Jose Mourinho's side surged to victory thanks to some neat interplay and Gennaro Gattuso's bizarre sending off.
Thiago Motta coolly curled in the first goal on 29 minutes after quick passes from fellow close-season signings Samuel Eto'o and Diego Milito.
Former Genoa frontman Milito then doubled the lead from the penalty spot at a packed San Siro.
Gattuso had hauled down the runaway Eto'o to concede the penalty and the Inter bench, who were initially jumping for joy, reacted furiously when he was only booked.
The Italy midfielder then asked to come off with an injury but substitute Clarence Seedorf was not ready, meaning Gattuso stayed on the pitch long enough to hack down surprise debutant Wesley Sneijder and finally receive his marching orders.
HORROR HALF
Rookie Milan coach Leonardo's horror half was compounded by Inter right back Maicon finishing off another fine one-two move with Argentina's Milito, to make it 3-0 just before the break.
In the second half Leonardo threw on Seedorf, new signing Klaas Jan Huntelaar and Massimo Ambrosini, who started on the bench despite being club captain following the retirement of the watching Paolo Maldini.
The trio stemmed the tide for a while until Dejan Stankovic blasted in from 25 metres midway through the second period to further embarrass Milan, who had looked bright in their 2-1 win at Siena on the opening day last Saturday.
Inter coach Mourinho had said Dutch playmaker Sneijder would not play, having only signed from Real Madrid on Friday, but it was a typical ploy from the charismatic Portuguese.
Sneijder had two good efforts from distance but wasted some dead ball situations after starting in place of Ghana midfielder Sulley Muntari, who Mourinho has said may be suffering with his energy levels because he is fasting for Ramadan.
In Saturday's early game, promoted Bari drew 0-0 at home to last season's strugglers Bologna on a sun-scorched pitch.
Bari, due to be taken over by an American tycoon while an Albanian businessman's bid for Bologna has fallen through, had Ferdinando Sforzini sent off for protesting in injury time.
