Petros seized on the short pass and squared for Danilo to side-foot into the empty net after 32 minutes.
Corinthians, who had goalkeeper Cassio sent off for time-wasting 11 minutes into the second half, still held on to win the first derby held at Palmeiras's new Allianz Parque.
But events on the pitch were once again overshadowed by violence outside the ground before kick-off.
Fans ran for safety as others threw chairs and missiles at riot police, who launched smoke bombs to disperse the crowd.
The Paulista Football Federation had ordered the match to be played with only home supporters present but Corinthians won a court injunction and several thousand of their fans were allowed in.
The result means that Palmeiras have won just one of their first three Paulista state championship games in spite of signing more than a dozen players in the close season, including former Brazil internationals Ze Roberto and Arouca.
Corinthians, who rested some first-team regulars ahead of their midweek Libertadores Cup visit to Colombia, have six points from six, one of only two teams with maximum points.
(Reporting by Andrew Downie,editing by Ed Osmond)
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