Brazilian defender Dani Alves, who joined from Barcelona in the close season, fired in from 25 metres with the ball taking a wicked deflection off Goldaniga's leg to hand Juve their fifth win in six league matches in a scrappy encounter.
Juventus, who had crushed Cagliari 4-0 in midweek with Alves on target, struggled with a tight Palermo defence in the first half, with both Gonzalo Higuain and Mario Mandzukic failing to put them ahead with several good scoring chances.
Alves finally broke the deadlock four minutes after the restart with his deflected strike beating Palermo keeper Josip Posavec to put the visitors ahead and the effort awarded as an own goal by Goldaniga.
Mandzukic should have doubled their lead on two occasions late in the game but both times Croatian Posavec denied his fellow countryman.
Juventus, who never hit top form, move up to 15 points, with second-placed Napoli, on 11, taking on Chievo Verona later on Saturday.