The Grifoni came into this match buoyed by a win over Lazio in Rome on Sunday and Palacio's first-half double followed by Kevin Constant's 79th-minute header took them above Juventus and Udinese on goals scored.
Alberto Malesani's team were straight onto the front foot as Kakha Kaladze's header from Miguel Veloso's free-kick drifted just wide in the second minute and Dario Dainelli blasted over from close range following a Veloso corner.
Palacio gave a hint of what was to come with a smart turn and shot in the ninth minute, but fellow Argentinian Mariano Andujar was equal to it in the Catania goal.
Catania created an opening after 10 minutes as Alejandro Gomez fizzed a low ball across the box but no one was able to apply the finish. Five minutes later Maxi Lopez's shot proved too weak truly to test Sebastien Frey in the Genoa goal.
The French goalkeeper was worked far harder after 25 minutes, performing heroics to deny Lopez from close range and then even better to block Marco Biagianti's follow-up.
Frey's saves looked all the more vital in the 29th minute when Veloso centred for Palacio, who brought the ball under his spell before drilling it low to Andujar's left.
Andujar reacted smartly to keep out Andrea Caracciolo's right-foot effort from Cristobal Jorquera's cross.
Genoa did double their lead in the 34th minute however when a Caracciolo shot was blocked on the line by Nicolas Spolli and Palacio was on hand to turn the ball home.
The Catania goalkeeper was called upon twice more to prevent any further first-half scoring, first denying Cesare Bovo and then frustrating Palacio's hat-trick quest by blocking his effort from 10 yards.
Gennaro Delvecchio fired over the first chance of the second period from the edge of the Genoa box and Pablo Ledesma scuffed a shot which drifted wide as the match started to get away from the visitors.
Genoa came close to adding a third as the game approached the hour mark, Spolli making a great last-ditch challenge on Caracciolo after a clever pass from Palacio.
Delvecchio tried his luck with a wild effort for Catania midway through the half, but Constant nodded home a third for Genoa with 11 minutes to go after good link-up play from the ever-inventive Palacio.
Juraj Kucka drilled a 35-yard strike goalwards in the 87th minute as Genoa pushed for a fourth, but the margin of victory was enough to ensure their place at the Serie A summit.