The visitors, without a Serie A win this term prior to the game, were quickly ahead when skilful Argentine playmaker Javier Pastore pounced after Marco Storari could only parry Mauricio Pinilla's shot on two minutes.
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Highly-rated Pastore, who also hit a post, pulled the strings all game and when Storari pushed away his fierce effort in the second half, Josip Ilicic was on hand to score the second.
Cesare Bovo's 85th minute freekick then gave silent Juve fans a familiar sinking feeling.
Vincenzo Iaquinta headed in late a consolation for the hosts, who also hit the woodwork through evergreen forward Alessandro Del Piero and had a good penalty appeal turned down.
Palermo have now won at Turin's Stadio Olimpico on their last three visits and also beat Juve at home last term as the twice European champions spiralled down to a shock seventh place finish in Serie A.
The start of this season under new coach Luigi Del Neri has been little better for Juve, who beat bottom side Udinese 4-0 on Sunday but lacked quality throughout against Palermo with new signings Milos Krasic, Simone Pepe and Fabio Quagliarella all flattering to deceive.
Juve, in the bottom half on four points from four games like Palermo, spent big in the close season but fans fear Italy's most successful domestic team have bought good rather than great players who could struggle to reverse the club's decline since a 2006 match-fixing demotion.
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