Palacio leads Inter past AC Milan
Palacio struck four minutes from time to send three quarters of San Siro into a frenzy.
Andrea Poli had missed an open goal for Milan, while Inter had a strong penalty claim turned down shortly before halftime after a clumsy challenge from Cristian Zapata on Rodrigo Palacio.
Mario Balotelli, who spent a troubled few seasons at Inter before a move to Manchester City, had a number of chances against his former club.
Milan midfielder Sulley Muntari was sent off in stoppage time after he shoulder-barged Zdravko Kuzmanovic for time wasting.
''We were obviously tired in the last 20 minutes,'' Milan coach Massimiliano Allegri said. ''I didn't manage to do my last substitution when I wanted to because the ball didn't go out. I don't have to reproach the lads for anything, Inter had a good game, especially defensively. I'm disappointed because it was a balanced game apart from in the last 20 minutes.
''A derby is a derby but it was even more important to win after three draws and a bad defeat,'' Inter coach Walter Mazzarri said.
There was an odd atmosphere at San Siro ahead of kickoff as Milan fans had been banned from bringing in their pre-match choreography and Inter supporters had removed their banners too in a show of solidarity.
Riccardo Saponara started for the first time for Milan, having played just 24 minutes in two substitute appearances. Sapanora almost helped give Milan an early lead with a through ball for Balotelli, but Juan Jesus deflected the Italy striker's effort wide of the right post.
Both sides had opportunities but failed to really test either goalkeeper as Milan dominated for large periods.
Milan should have taken the lead just before the half hour mark when Inter goalkeeper Samir Handanovic flapped at a corner and the ball fell to Poli, who incredibly blasted over from 10 yards.
Balotelli had two good chances shortly after halftime but was first denied by a fine one-handed save from Handanovic before a volley was deflected narrowly wide.
Inter nearly broke the deadlock 10 minutes from full time but Christian Abbiati pulled off a double save to deny first Palacio and then Fredy Guarin.
Palacio scored shortly afterwards, flicking the ball in from six yards with a backheel from Guarin's pass