Palacio nodded in the only goal of the game on the half-hour mark as Inter returned to winning ways after draws in their previous two league games.
The outcome in Milan has kept the Nerazzurri in fifth place, just one point adrift of fourth-rankedFiorentina, who lost 1-0 at Juventus earlier in the day.
Inter, with just a single defeat at home this season, went into the contest looking to capitalise on the absence of five regular defenders for Torino who were either injured or suspended.
But a side that has struggled to hit the back of net did not make the most of their chances.
Palacio's goal was just Inter's seventh of 2014.
Inter were fortunate not to fall behind in the 14th minute when a defensive distraction left Ciro Immobile unmarked in the heart of the area.
Fortunately for the hosts, he headed a cross over the bar.
At the other end, Palacio got behind Fredy Guarin's cross and his header was kept out by Torino goalkeeper Daniele Padelli.
Inter went ahead in the 30th minute when Palacio played a one-two with Esteban Cambiasso in the box and nodded past Padelli from close range.
Before half-time, Cambiasso released Hernanes into the area but his left-footed shot from 25 yards went wide.
The visitors almost pulled level early in the second half when Giuseppe Vives spotted Alessio Cerci in the box but his shot towards the far post was kept out by Inter Milan goalkeeper Samir Handanovic.
Palacio should have scored his second of the afternoon in the 63rd minute when Hernanes sent a cross into the heart of the area but he blasted the ball over the bar.
Inter wasted another good chance to kill the game off with 10 minutes remaining when Yuto Nagatomo found Hernanes in the box and the Brazilian's diagonal shot went wide.
The hosts held on for victory, though.