Kalidou Koulibaly scored an own goal in the second minute of stoppage time to hand Juventus the three points in Turin.
Massimiliano Allegri held meetings with Juventus' hierarchy earlier in the week during which a clear disagreement between the two parties emerged.
Moise Kean, 19, came on as a substitute in Turin and three minutes later scored his third league goal of the season.
Juventus open up a 12-point lead at the top of Serie A ahead of Napoli.
Palermo has nurtured top players such as Argentine internationals Paulo Dybala and Javier Pastore and Uruguay forward Edinson Cavani.
Cristiano Ronaldo equalised from the spot before blasting home a magnificent second to secure a ninth win in 10 Serie A matches for Juventus.
Juventus have maximum points after three games in Group H, and host Mourinho's side in Turin next.