The Nerazzurri made the breakthrough as early as the fourth minute through Walter Samuel.
The Inter centre-back's Argentine compatriot Diego Milito almost doubled his side's advantage three minutes later.
The 33-year-old striker intercepted Abbiati's pass out of his penalty area and shot at the Rossoneri goal, but it was saved by the goalkeeper.
Inter continued to dominate proceedings at the San Siro, with Milito proving to be a handful for the Milan defence.
Three minutes later the visitors went close, Milito placing a shot-cum-cross along Milan's six-yard box but there was no one in an Inter shirt to turn it home.
Montolivo thought that he had given Milan the lead six minutes from the interval with a brilliant volley, but it was ruled out because of a foul from Urby Emanuelson on Handanovic.
Bojan Krkic then tested Handanovic with a shot from inside the area on the stroke of half-time.
The second half started on a bad note for Inter, as full-back Yuto Nagatomo was sent off just three minutes into the restart for a second bookable offence.
The numerical advantage handed the initiative to Milan, for whom Montolivo took two shots in two minutes.
Emanuelson crafted an inviting cross for Robinho on the hour mark, but the Brazilian forward's header had little conviction.
Four minutes later Montolivo forced Handanovic into making a good save with a fierce strike from 30 yards, and tested the Inter goalkeeper again in the 66th minute.
Milan continued dominating the proceedings, with Giampaolo Pazzini and Emanuelson coming close, but it was not enough for them to stop Inter from bagging maximum points.