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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Cesare Bovo's 85th minute freekick then gave silent Juve fans a familiar sinking feeling.
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.
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.
