Ronaldinho's first-half header gave Milan a 1-0 victory over arch-rivals Inter as the Nerazzurri suffered their first defeat under Portuguese coach Jose Mourinho. The Brazilian playmaker, who joined Milan from Barcelona in the close season, looked on course to regain the form that saw him named the World's best player twice. He had a powerful shot smothered by Inter's Brazilian goalkeeper Julio Cesar midway through the first half. Ronaldinho scored what proved to be the winner nine minutes before the break as he rose above two challengers to head home Kaka's inch-perfect cross from the right. Inter's bid to grab the equalizer was hindered by the dismissal of Argentinean defender Nicolas Burdisso, who collected a second booking in the 77th minute. Italy defender Marco Materazzi, who had been substituted, was also sent off in the closing stages for dissent. Title holders Inter slipped to fourth spot in the league table with 10 points, two behind surprise leaders Lazio, who defeated Torino 3-1 earlier on Sunday. A brace from Argentine forward Mauro Zarate and a strike from Goran Pandev handed Delio Rossi's men a valuable win.