The Nerazzurri gained all three points in Sicily.
The hosts put faith in their youth, coming off two disappointing 3-2 losses against Brescia and Sparta Praha, with coach Delio Rossi giving starting berths to Ezequiel Munoz, as well as Josip Ilicic and Abel Hernandez supported by Javier Pastore up front.
The visitors had to do without Wesley Sneijder, so Dejan Stankovic filled in the playmaker role. Meanwhile, right-back Maicon returned to the line-up after missing last week's Serie A win over Udinese.
It was a hectic start, as the ball moved qiuckly from end to end, but clear cut chances were not present in the first ten minutes.
Stankovic nearly opened the scoring on 12 minutes, Armin bacinovic went down lightly and the referee waved play on and the Serbian was quickest to react from 30 yards as he hit the ball off the crossbar as the visitors were starting to pile on the pressure.
Goalkeeper Salvatore Sirigu has come under fire for his performances recently, but made a crucial challenge on Milito's cross that stopped Eto'o from tapping the ball into the net.
Palermo scored on their first dangerous chance. Ilicic stole the ball in midfied and glided past the Inter midfield on the counter to lay off for Pastore in the area, Julio Cesar did well to block the shot but could do nothing as Ilicic pounced on the rebound on 28 minutes.
The Beneamata nearly pulled the goal back immediately, but Eto'o's shot was cleared with the goal gaping. Meanwhile, Milito's continued to struggle after being fed twice in the area - once being blocked by Sirigu and then shanking wide.
Despite the champions' dominance in possession, they could not find an equaliser and went into half-time trailing.
The quiet Hernandez finally found some space early in the second-half to shoot from a tight angle, though Julio Cesar was well positioned and saved with ease.
Palermo should have had their second on 50 minutes, Inter were caught up field and a brilliant swith to Cassani galloping down the right opened up the visitors' defence. His cutback found Armin Bacinovic breaking through, but Cesar got down well to stop his rather tame effort.
It was a very open game and Milito somehow missed his third good chance of the afternoon as he played a give-and-go with Stankovic on the edge of the area.
The Nerazzurri finally found their goal from the likely source of Eto'o after an hour. Milito set up the Cameroon international, who turned centre-back Munoz and finished into the bottom corner.
Pastore had been shackled for long portions, but he missed a golden chance after collecting Antonio Nocerino's chip over the back-line, shooting over the bar.
Inter took the lead with a brilliantly well-worked goal, Stankovic's backheel found Maicon, who returned the ball to the Serbian. 'Deki' then squared for Eto'o for the tap in and it was 2-1 for the Nerazzurri.
The Rosanero had a penalty shout with Cassani, but despite Cristian Chivu's clear push the linesman had already raised his flag for offside. The Italian international was booked for his protests.
With 12 minutes remaining, the changes were rung as Rossi threw on Massimo Maccarone in search of a second goal and Davide Santon replaced Stankovic for his first appearance of the season.
The Argentine playmaker Pastore had the best chance of the latter stages, smashing his drive against the post on 88 minutes, but it was not to be for the hosts as they fell to their third consecutive loss in all competitions.
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