Argentine forward Diego Milito set the champions on their way with a diagonal strike on 10 minutes.
They then spent long periods under intense pressure in their own half after Dutch playmaker Wesley Sneijder was sent off for dissent in the 27th minute before Goran Pandev doubled the lead with a free-kick in the 65th.
"I'm happy to have given my contribution," Julio Cesar told Sky television. "It's not easy to play practically the whole game with 10. My team mates showed how strong this group is today."
Milito took advantage of a blunder by Milan's Ignazio Abate, who headed the ball into his path when trying to cut out a cross, to give them a deserved lead.
Inter were dangerous on their rare forays forward though and Pandev had struck the woodwork at the end of a counter-attack before scoring his side's second. Cesar capped off a great night for Jose Mourinho's men with a superb penalty save.
Palermo climbed to fifth with a 3-0 home win over Fiorentina thanks to a first-half double by 19-year-old Uruguayan forward Abel Hernandez and Igor Budan's acrobatic effort just before the hour.
The Sicilians' victory means Juventus drop to sixth after their miserable run continued with a 2-1 home defeat by third-placed AS Roma on Saturday, leaving coach Ciro Ferrara in danger of losing his job.
Napoli consolidated fourth place with a 2-0 win at lowly Livorno. The Tuscan side's coach Serse Cosmi quit after the game, citing differences with the club president.
Sampdoria boss Luigi Del Neri's surprise decision to drop out-of form- forward Antonio Cassano seemed to pay dividends as the early pacesetters twice came from behind to beat struggling Udinese 3-2 and halt a slide in form.
