The Nerazzurri went from 2-0 down to 3-2 up.
Brazilians Julio Cesar and Coutinho both made returns from injury, while defenders Andrea Ranocchia and Davide Santon replaced the suspended Cristian Chivu and Ivan Cordoba at the back. New signings Pazzini and Houssine Kharja started on the bench.
Palermo's line-up had no surprises as they stuck with their usual trident attack of Javier Pastore and Josip Ilicic supporting Fabrizio Miccoli.
It was Miccoli who opened the scoring after just five minutes. Pastore did not play the ball knowing he was in an offside position and Mattia Cassani burst through past the bewildered Santon who was too easily beaten. It turned into an easy tap-in for the captain from six yards. Inter appealed to no avail.
The hosts responded well, taking the match to their opponents, but struggling to break through the Rosanero's last line of defense despite plenty of possession in the early stages.
Defender Ezequiel Munoz then blocked a certain goal from Coutinho, after the Brazilian redirected a cutback from close range.
Despite all their dominance, Inter amazingly found themselves two goals behind. A cross found Antonio Nocerino, who skipped past Maicon and fired low and hard under Julio Cesar to give the Sicilians their second goal on their second shot on target.
At the other end it was madness, both Javier Zanetti and Diego Milito had efforts blocked away at the last second, while on the counter Santon cleared the ball off the line after a rebound had their shot stopper in no man's land, and Pastore smashed against the post. The exciting clash went into half-time with the visitors 2-0 up.
Both recent arrivals Pazzini and Kharja came on to start the second-half to make their debuts as youngsters Coutinho and Santon made way after a relatively poor first 45 minutes.
Palermo goalkeeper Salvatore Sirigu made a crucial save, denying Eto'o's set piece from flying into the bottom corner from the edge of the area after Pazzini had been fouled on 51 minutes. He then denied Milito with another good stop minutes later.
Pazzini and Kharja made good first impressions. The Italian perfectly shielded the ball from Munoz and turned to fire low into the net after collecting the ball from the Moroccan midfielder in the center of the area.
Somehow Julio Cesar kept the ball out when Miccoli's whipped in corner took a deflection off Zanetti, but the veteran made a brilliant reaction stop. That was the Palermo striker's last action as he made way for Pajtim Kasami. The substitute had an immediate impact being fouled in the area by Thiago Motta after an hour of play, but Pastore's weak penalty was saved by Julio Cesar. It was the Rosanero's first penalty awarded in Serie A this season.
Pazzini's debut got even better as he headed in the equalizer. Maicon's cross from the freekick found the former Sampdoria man and his glancing header put Inter on level terms at 2-2 with just under 20 minutes remaining.
The match was completely turned on 75 minutes. Pazzini drew a contentious foul in the penalty area and Eto'o dispatched the spot-kick into the net to make it 3-2.
The last chance fell to Federico Balzaretti who saw his volley deflected away by both Maicon and Julio Cesar and could not believe it had stayed out.
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