Catania managed a late consolation goal from Franceso Lodi but missed the chance to go sixth in their first defeat after four consecutive wins.
Palermo, who moved away from the relegation zone and up to 14th place with 14 points from 14 games, took the lead in the ninth minute after enjoying the better of the opening exchanges.
Catania's Nicolas Spolli slipped while trying to cut out an Ezequiel Munoz cross, wrong-footing veteran defender Nicola Legrottaglie in the process and allowing Miccoli space and time to place his shot into the net from the edge of the box.
The home side looked confident, pressing the disjointed visitors and coming close to a second goal when Franco Brienza ran into the area, shrugged off two defenders and struck a powerful shot against the bar.
Catania, who remain seventh with 19 points, had their moments, notably a Sergio Almiron effort from distance and a wonderful curled Lodi free-kick just before the break, but struggled to get any grip on the match.
Ilicic made it 2-0 in the 48th minute, after Brienza found the Slovenian courtesy of some loose Catania defending, scoring with a right-foot shot from just inside the area.
On the hour mark, with Catania again caught napping on the break, Ilicic ran from the halfway line, beat the sluggish Lodi and hit an angled drive past the unfortunate Mariano Andujar in the visitors' goal.
Lodi's powerful 70th-minute free-kick gave Catania some hope but the hosts responded and nearly got a fourth goal when Spolli cleared Michel Morganella's close-range effort off the line.