The forward struck the only goal of the game as Walter Mazzarri's side capitalised on the Viola's defeat to Juventus earlier on Sunday
Walter Mazzarri's side are unbeaten in five matches after further denting the ambitions of a Torino side they now lead by eight points.
Palacio, who scored twice in October's reverse fixture, haunted the visitors again with a clever header half an hour into the game.
Torino had a better time of it in the second half as the game opened up, but Inter stood firm as they marked their 106th anniversary with a victory.
Alessio Cerci and Ciro Immobile almost combined to create an opening after eight minutes as the hosts' defence made a shaky start.
After struggling to deal with a number of deliveries, Inter produced another poor clearance that fell to Cerci, who could only fire over from inside the area.
Fredy Guarin's powerful drive was blocked well by a combination of Guillermo Rodriguez and Giuseppe Vives, and Palacio saw a header palmed wide by Padelli as the home side gradually grew into the game.
However, Palacio did open the scoring with a well-angled header from a delightful Cambiasso pass just before the half-hour mark.
It was deserved, given Inter's strong period of play from the 10-minute mark and Cambiasso was at the centre of things again soon after - almost finding Mauro Icardi in a dangerous position.
Hernanes almost doubled Inter's advantage five minutes before the break with an effort from distance, while Cerci was unable to reach a long ball from Immobile that could have provided him with a chance to level.
In a lively opening to the second half, Rolando headed straight at Padelli from Hernanes' delivery and Handanovic was forced into an early save from Immobile's effort.
Migjen Basha rippled the side-netting with a well-struck effort from distance but Inter stood firm and ensured Torino's goal drought now stands at three games.