Serie A - Inter rescue win through Eto'o double
Josep Ilicic had earlier helped the hosts to a first half lead against the run of play.
Every player in Benitez's eleven had been part of the Jose Mourinho era, and they lined up in a customary 4-3-3 formation, but despite dominance in possession, they could not translate their advantage into a lead.
Dejan Stankovic rattled the woodwork after twelve minutes with a rasping, swerving volley, but that aside the visitors were wasteful and unthreatening from distance.
Eto'o came within a hair's breadth of turning in Diego Milito's cross halfway through the first half, but Palermo then struck at the other end.
27 minutes had passed when a flowing move culminated in a shot from Antonio Nocerini - Julio Cesar made a good save but the ball rebounded into Ilicic's path the forward had no trouble slotting it past the stranded goalkeeper.
Inter responded immediately and might have been level had it not been for a desperate, scrambled clearance from an Eto'o shot.
Moments later Salvatore Sirigu was called into action to make a brave save against the onrushing Milito, but despite Inter's control over much of the game, Palermo held firm at the back and remained a menace on the break.
That pattern continued in the second half, as Abel Hernandez probed for the home side and Armin Bacinovic squandered a good chance to make it two for the hosts after 49 minutes.
Inter were not to be denied, however, and just after the hour Eto'o masterfully skipped around Ezequiel Munoz before burying a shot low past Sirigu.
Javier Pastore had half a chance for the home side before the Nerazzurri found their winner, Eto'o slamming home Stankovic's cut-back midway through the second half.
And in the final minutes another wave of pressure led to Pastore rapping the post.
For the most part, however, Inter were the better side, and Benitez will be delighted to have got three points in one of the tougher away fixtures on the Serie A calendar.
The win provisionally leaves his side second in the table behind surprise package Cesena, with Sampdoria still to play against Napoli in the evening fixture.