The captain was on target twice in Sicily as he inspired his team to come back from behind and seal a memorable win
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The Sicilians came from behind twice, with Miccoli scoring a double as his side edged a tense thriller.
Diego Milito gave Inter the lead against the run of play in the first half before Miccoli responded for Palermo. Milito scored a penalty, but Abel Hernandez restored parity just minutes later.
After a flurry of exchanges, it was Miccoli and then Mauricio Pinilla who made it 4-2 before Diego Forlan grabbed a late consolation.
"It was a sublime game and we could not have asked for a better start," Miccoli told Sky Sport Italia after the game.
"I want to thank my team-mates. I am very satisfied as I always want to do my best.
"I am proud to be captain both on and off the pitch."
The result sees Palermo move into fifth in Serie A while Inter are 14th after week one of Serie A.