AC Milan have lost their first Serie A match since October 2011 as Inter claimed a 1-0 win in the Milan derby.
Alexandre Pato had an early opportunity to give the hosts the lead, but his snatched shot blazed over the crossbar.
As Milan asserted their dominance, Kevin-Prince Boateng's half volley flew off target.
The hosts had the final say of the half when Mark Van Bommel's powerful drive crashed back off of the bar.
Alvarez tried to catch Abbiati out from 30 yards on the hour, but the keeper managed to save.
Another Milan substitute, Robinho, nearly found an equaliser in the final 10 minutes, but his poked effort was stopped by the feet of Cesar.