Inter moved top of Serie A after winning 3-0 at Catania while Mario Gomez scored his first Serie A goals and Giuseppe Rossi made it three for the season as Fiorentina defeated Genoa 5-2.
Milan bounced back from last week's defeat at Hellas Verona with a 3-1 win at home to Cagliari in an entertaining evening featuring 32 goals in eight games.
It was one-way traffic in Sicily as Walter Mazzari's Inter showed that they have put last season's troubles behind them.
Smartly worked goals from Rodrigo Palacio, Yuto Nagatomo and Ricky Alvarez helped them beat a fired-up Catania team who have yet to get a point after two defeats.
Alberto Aquilani gave Vincenzo Montella's Fiorentina the lead at Genoa after 10 minutes before Giuseppe Rossi scored his second in as many games four minutes later and Gomez tapped in his goal four minutes before the break.
Alberto Gilardino gave the home side some hope nine minutes after the break with a stunning volley, but Rossi tapped in his second almost immediately afterwards.
Francesco Lodi reduced the deficit again on the hour with a penalty following a foul on Gilardino, but an injury time penalty from Mario Gomez ruined Genoa's celebrations for their 140th anniversary, in which cricket was played on the Stadio Luigi Ferraris pitch before the match.
The club's official name is Genoa Cricket and Football Club, and it has a cricket team which was re-established in 2007 and plays in Italy's top division.
Goals from Robinho, Philippe Mexes and Mario Balotelli were enough for Milan against a plucky Cagliari team.
Brazilian Robinho and Mexes put Massimiliano Allegri's side two goals up after half an hour, only for Marco Sau to pull one back for the away side three minutes later.
However, Balotelli's first league goal of the season in the 62nd minute put the result beyond doubt.