Adriano fired Inter ahead with a fine solo goal in the 32nd minute and added two more after the break. Milan struggled on a rain-sodden pitch at Ascoli, going behind to a Mirko Cudini goal before Andriy Shevchenko's 20-metre drive gave them a point.
The new Roma coach, Luciano Spalletti, made a winning start with a 3-0 victory at Reggina and Lazio beat Messina 1-0 at the Olympic Stadium.
Portuguese winger Luis Figo was the centre of attention at the San Siro as he made his full debut for Inter but it was the more familiar face of Adriano that provided the joy for the home fans hoping to end their 16-year wait for a title. The powerful Brazilian opened the scoring by chasing a ball 40 metres out to the touchline before cutting inside and then unleashing a fierce drive into the near post. Serbian Dejan Stankovic set up the second in the 68th minute with a well weighted ball into the area which Adriano brought down with ease before slotting home.
Chilean substitute David Pizarro took most of the credit for Inter's third goal with a tricky solo run into the area before a short pass to the Brazilian who screwed the ball home. Milan fell behind in the 58th minute when Dida pushed out a header from Fabio Quagliarella and Cudini reacted to beat the Brazilian keeper. Five minutes later, Milan levelled when Shevchenko rattling home a powerful drive.
Goals from the Brazilian Mancini, Italy midfielder Daniele De Rossi and an injury-time strike from debutant Democratic Republic of Congo forward Shabani Nonda gave Roma a 3-0 win at Reggina.
Udinese beat a determined Empoli 1-0 while Macedonian striker Goran Pandev scored in Lazio's 1-0 win over Messina.
Meanwhile, the Italy striker Cristiano Lucarelli wants to discuss his future with the president of Livorno, Aldo Spinelli, after being linked with a move to Tottenham Hotspur.