Inter have seven points from three games, level with promoted Cesena, who beat Lecce 1-0 despite the referee saying he had wrongly sent off Giuseppe Colucci in the first half after a case of mistaken identity.
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Cameroonian Eto'o was often overshadowed by strike partner Diego Milito in Inter's stunning treble triumph last term but their roles have been reversed so far this season.
While Milito has struggled, Eto'o has started his second campaign at Inter in supreme form and again dug Rafael Benitez's inconsistent side out of a hole.
Slovenian Josip Ilicic put struggling Palermo ahead in the first half before Eto'o produced a piece of magic to equalise on 62 minutes following Milito's pass and soon finished off a fine move involving Dejan Stankovic and Maicon to seal victory.
"The team played a spectacular first half, we controlled everything apart from their goal," Inter coach Rafael Benitez told Sky TV after playing without the injured Wesley Sneijder.
"We found it a bit harder in the second half but we got two goals. We have to find a bit more balance, but we're improving."
Eto'o scored the winner in last weekend's 2-1 win over Udinese and salvaged a 2-2 draw at Twente Enschede in the Champions League in midweek.
CRAFTY BACKHEEL
Sampdoria could have topped the standings with victory but lost 2-1 at home to Napoli in a game that burst into life late on.
Antonio Cassano's debatable penalty put the hosts ahead on 78 minutes but Napoli, managed by former Samp boss Walter Mazzarri, quickly turned the tables when Marek Hamsik converted a clever free-kick and Edinson Cavani poked in at the near post.
Juventus, whose poor form last term continued into the new season, bounced back with a 4-0 win at pointless Udinese, striker Fabio Quagliarella scoring against his former club.
Leonardo Bonucci grabbed the opener before Quagliarella's crafty backheel, a thunderbolt from Claudio Marchisio and a fourth from Vincenzo Iaquinta, whose aggressive goal celebration was not appreciated by his former Udinese employers.
Striker Marco Borriello netted his first league goal for AS Roma as they raced into a 2-0 lead against Bologna but Claudio Ranieri's faltering side allowed Marco Di Vaio to score two second-half goals and secure a 2-2 draw for the visitors.
Former Roma forward Luca Toni scored his first league goal for Genoa from the penalty spot in a 1-1 draw at Parma.
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