After Juventus were held to a disappointing 1-1 draw at home to Cagliari earlier, Milan could have pulled two points clear at the summit but instead ended the night in second place as Inter sounded their intentions in the race for the Scudetto.
A goal from Diego Milito in the 54th minute was enough to earn the designated visitors all three points at the San Siro and take them to within six points of the summit - and just five of their city rivals.
Unbeaten Juve started the weekend level on 37 points with Milan and looked set to pick up three more points after taking a seventh-minute lead through Mirko Vucinic in their match against Cagliari.
But Cagliari upset their hosts by drawing level just after half-time through Andrea Cossu.
Genoa came from behind to defeat high-flying Udinese 3-2 at the Stadio Luigi Ferraris.
Damiano Ferronetti put Udinese in front in the 13th minute, but goals from Andreas Granqvist and Bosko Jankovic early in the second half put Genoa in charge.
Rodrigo Palacio added Genoa's third before Antonio Di Natale pulled one back after the referee awarded a penalty for a challenge that saw Genoa captain Marco Rossi sent off.
Lazio ended a three-match winless run with a 2-0 win over 10-man Atalanta.
Hernanes put Lazio ahead from the penalty spot in the 20th minute after Stefan Radu was brought down inside the area by Atalanta's Andrea Massiello.
The visitors were then forced to play a man down as defender Stefano Lucchini was sent off after 52 minutes for a second bookable offence.
Jonathan Biabiany, Francesco Valiani and Sebastian Giovinco bagged the goals as Roberto Donadoni's encouraging start to his reign as manager of Parma continued with a 3-1 win over Siena, who replied through Paolo Grossi.
Palermo's winless run on the road this season continued in Serie A as they lost 1-0 at Chievo, Paolo Sammarco netting the only goal of the game in the 50th minute.
At the foot of the table, Cesena returned to winning ways with a 3-1 defeat of fellow relegation battlers Novara.
Adrian Mutu put Cesena ahead in the 20th minute before adding his second from the penalty spot after Antonio Candreva was brought down by Michel Morganella.
Cesena went into the break 3-0 up after Leandro Rinaudo deflected the ball into his own net.
The hosts should have extended their advantage after the hour mark but Candreva saw his penalty saved by Novara goalkeeper Samir Ujkani. Substitute Takayuki Morimoto then scored a consolation goal two minutes from time.
Lecce hauled themselves off the foot of the standings with a smash-and-grab 1-0 victory on the road at Fiorentina, David Di Michele with the only goal from the penalty spot in the 66th minute.
Sunday's Serie A Results
Saturday's Serie A Fixtures
Monday's Serie A Fixture
Napoli vs Bologna