Milan took the lead after 17 minutes through Andrea Pirlo's stunning free-kick before Julio Cruz levelled the scores in the 36th minute and Esteban Cambiasso was gifted his side's second on 63 minutes.
Inter are unstoppable in Serie A this season but the defending champions showed reverence to their city rivals as they welcomed the returning World Club Champions onto the pitch with a guard of honour.
They seemed to be showing the same deference in the game as both sides started cautiously before the match sprang into life just after the quarter-hour mark.
Milan were awarded a free-kick just outside the area which Pirlo, who played two seasons at Inter without scoring, fired into the top left corner giving Julio Cesar no chance.
Inter should have equalised just three minutes later as Cruz put a tantalising cross into the area.
Dida got a hand to it but could only watch from the ground as it fell to Luis Jimenez who saw his close-range effort crash back off the crossbar from a tight angle.
After 32 minutes, newly-crowned World Player of the Year Kaka almost doubled the Rossoneri's advantage as he dribbled half the length of the pitch into the area but found himself crowded out before he could get a shot in.
But four minutes later Inter drew level.
Cambiasso pulled the ball back to Cruz on the edge of the area who squeezed the ball through three Milan defenders and past the outstretched Dida into the bottom left corner.
Inter should have gone ahead in the 57th minute as Cambiasso wasted a glorious chance - putting his shot well wide of the left upright from the edge of the area.
But six minutes later Dida and Maldini combined to gift the Nerazzurri the lead.
The veteran defender's poor clearance fell to Cambiasso at the edge of the area who scuffed his shot towards the centre of the goal.
Dida should have saved comfortably but the former Brazil keeper dived too far to his left and it somehow squeezed past him.
The goal seemed to deflate Milan and another Rossoneri goal seemed even less likely.
Two minutes from time Ambrosini missed a golden opportunity to snatch a point for his side as he fired Serginho's shot wide from close range.
