Parma's Francesco Modesto struck the winner against Napoli eight minutes from time after Napoli's Giuseppe Mascara had equalised following Massimo Gobbi's 57th-minute opener.
Milan's Antonio Nocerino, scoring against his former club, Robinho and Antonio Cassano were all on target as Milan cruised past a disappointing Palermo.
Earlier, Inter suffered their fourth loss in their six Serie A matches this season, going down 2-1 at Catania.
Napoli, who host Bayern Munich in the Champions League on Tuesday, looked a pale shadow of the side that had stormed the San Siro two weeks ago in defeating Inter Milan 3-0.
After a lacklustre first half Massimo Gobbi put Parma ahead just before the hour mark, swapping passes with Stefano Floccari before slotting the ball past Morgan De Sanctis.
Napoli, who had created little against a well-organised Parma side, equalised with 15 minutes to go when substitute Giuseppe Mascara slipped the ball under goalkeeper Antonio Mirante after a brilliant flicked pass from Ezequiel Lavezzi.
But Parma silenced the San Paolo faithful with eight minutes left when Modesto tapped in Sebastian Giovinco's enticing cross after a fast counter attack.
Napoli coach Walter Mazzarri felt his players lacked sharpness after returning from international duty.
"Parma played a strong, defensive game," he told Italy's Sky Sport channel. "They looked much fresher. The referee didn't help either by blowing up all the time and breaking our flow.
"It's a shame Lavezzi doesn't score more. He likes dribbling but perhaps doesn't have that coolness in front of goal that's associated with top goal-scorers."
Milan welcomed back the fit-again Robinho allowing coach Massimiliano Allegri to play the attacking trident that hit it off so well last season with the Brazilian playing just behind Swede Zlatan Ibrahimovic and Italian Antonio Cassano.
Cassano, who scored a double for Italy on Tuesday before threatening to quit the game in three years, had two copycat chances to open the scoring after 13 and 18 minutes but slipped the ball the wrong side of the post on both occasions.
Palermo, starting in fourth position after new coach Devis Mangia had inspired several stirring displays, offered little going forward and had keeper Alexandros Tzorvas to thank after 37 minutes when he twice parried fierce Robinho strikes.
The Greek could do nothing three minutes later though when midfielder Alberto Aquilani nodded Ibrahimovic's cross back across goal for Nocerino to tap into an empty net although he would not celebrate against his former club.
Robinho had no such qualms 10 minutes after half-time when he ran on to Ibrahimovic's pass and coolly flicked the ball past Tzorvas as a rampant Milan side cut the Rosanero defence open again.
After having a goal di
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