It leaves Palermo just outside the top four and they have also played a game more than their rivals.
Juventus now emerged as serious contender for a Champions League's place after they won three precious points from Inter.
Midfielder Alberto Aquilani had the first chance of the game, but chipped just over the crossbar.
Juventus winger Milos Krasic started the build-up for the goal, pulling the ball back for Frederik Sorensen to find Matri, who headed his cross past goalkeeper Julio Cesar.
Inter immediately went on the attack, but Esteban Cambiasso hooked his shot over the bar.
Early in the second half, Inter had its best chance, but goalkeeper Gianluigi Buffon punched Giampaolo Pazzini's header away.
Matri had a chance to add a second, but headed Krasic's cross wide from close range. He then took too long when Aquilani played him in and Maicon came back to clear.
Buffon had to rush off his line twice to stop Eto'o, and Matri then fired a shot wide from close range.
With two minutes remaining, Eto'o missed an open goal. He hit the bar from close range after Juventus' defense had failed to stop Maicon's low cross.
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