Juventus needed an unfortunate own goal from Edoardo Goldaniga to squeeze past Palermo while Napoli beat Chievo.
Juventus, who beat Cagliari 4-0, move to the top of Serie A after Napoli were held to a 0-0 draw at Genoa.
Mauro Icardi inspired a superb comeback win for Inter as they beat Juventus 2-1 on Sunday, while Roma lost at Fiorentina.
Borussia Dortmund hit six, while Juventus were held by Sevilla on the second night of Champions League group stage action.
Zlatan Ibrahimovic's goal-scoring start to life at Manchester United shows he is up there with the world's best, Gianluca Zambrotta says.
Gonzalo Higuain starred for Juventus with two goals as they beat Sassuolo 3-1 in Serie A on Saturday, as Napoli won 3-0 at Palermo.