Inter struck in the third minute with a Walter Samuel header and hung on despite playing nearly all the second half with 10 men to beat AC Milan 1-0 in a bad-tempered, scrappy but absorbing Serie A derby on Sunday.
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.
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 Ranieri, said: "This team has a lot of heart, that's what saw us through today."
Juventus and Napoli both have 19 points out of 21.
At Siena, Juventus midfielder Marchisio volleyed home from a partially cleared corner in the 85th minute to stretch champions Juve's unbeaten Serie A record to 46 matches.
Andrea Pirlo had put the title-holders ahead in the 14th minute with a low free-kick and hit the crossbar with another effort before Emanuele Calaio hit back for Siena in first-half stoppage time.
Siena, who began the season with a six-point deduction from the Calcioscommesse match-fixing scandal, are bottom with two points.
Miroslav Klose scored twice in 10 first-half minutes to help Lazio win 3-0 at Pescara after Brazilian playmaker Hernanes had given them a fifth-minute lead with a curling free-kick.
Calgliari, whose coach Massimo Ficcadenti quit on Tuesday, gave new manager Ivo Pulga a winning start thanks to a 74th-minute penalty converted by Brazilian Nene at erratic Torino.
Erik Lamela and Michael Bradley scored the goals in Roma's win.
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