A late goal by Claudio Marchisio gave Juventus a 2-1 win at lowly Siena and Napoli beat Udinese by the same score with Goran Pandev scoring the winner.
Cagliari won their first game of the season, 1-0 at Torino, and AS Roma finally managed their first home win as they beat Atalanta 2-0 to ease the pressure on coach Zdenek Zeman.
In the San Siro derby, Samuel scored with a diving header at the far post after Milan goalkeeper Christian Abbiati hesitated and failed to cut out Esteban Cambiasso's free-kick.
Milan created far more chances and were in almost total control after Inter had midfielder Yuto Nagatomo sent off for a second bookable offence three minutes into the second half.
The defeat left Milan with only seven points from their first seven league games of the season. Inter have 15, four behind leaders Juventus and Napoli who both won.
Milan, after selling several top players, have made a dreadful start to the season and continued with a farcical opening five minutes at San Siro.
Coach Massimiliano Allegri was still arguing angrily with the referee over the award of a free-kick to Inter when Cambiasso swung the ball over. Abbiati initially came then retreated, allowing Argentine defender Samuel, in his eighth season at Inter, to score with a free header.
ATTEMPTED CLEARANCE
Two minutes later, Abbiati kicked an attempted clearance straight to Diego Milito on the edge of the area but his effort was blocked by Daniele Bonera. The ball fell to the Argentine again but his weak header was saved.
Milan, officially the home side, took control as Kevin-Prince Boateng twice shot wide from dangerous positions and Bojan Krikic had a snap shot turned away by goalkeeper Samir Handovic.
Milan had also had the ball in the net in the 38th minute with a long-range shot by Riccardo Montolivo but the referee had already whistled after Urby Emanuelson clattered into Handovic, although Milan coach Massiliano Allegri did not see a foul.
"I have no idea what the referee whistled for on the Montolivo goal," he told reporters.
It was one-way traffic after Nagatomo was given a second yellow card for handball but Milan's attacking woes following the departure of Zlatan Ibrahimovic and Antonio Cassano, now with Inter, were exposed as they failed to take advantage.
Montolivo, the one bright spot for Milan, twice had Handovic in difficulty with powerful long-range drives but on each occasion Krkic failed to make the most of the rebound.
Substitute Giampaolo Pazzini twice missed the ball when he had close-range chances, Urby Emanuelson nearly scored with a shot across the face of the Inter goal and Robinho had a penalty turned down, leading to furious Milan protests.
"I cannot complain about the lads' performance. We just needed to be a little quicker and a little more precise," said Allegri. "We were just missing the result."
His opposite number Andrea Stramaccioni, who has won both his meetings with Milan since taking over last March to replace Claudio R
