The draw keeps Palermo within touching distance of a future in Serie A.
Defeat at the Stadio Angelo Massimino, which seemed inevitable following Pablo Barrientos' opener midway through the second half, would have left the Rosanero second from bottom and three points from safety.
Ilicic had other ideas, though, sparing his side's blushes and dragging the club to within a point of 17th-placed Siena with a confident finish four minutes into second half stoppage time.
Catania goalkeeper Mariano Andujar was subsequently dismissed as the hosts' frustration boiled over.
The home fans teased their rivals with banners mocking their possible relegation and that would perhaps be the best entertainment on offer through a dull first half.
Catania enjoyed the better chances with Sergio Almiron's swerving drive shaving the crossbar before Francesco Lodi's free-kick forced a fine save from Stefano Sorrentino.
The 17th minute saw Palermo go close as Ilicic loped into the area.
But the Slovenian became flustered at the crucial moment and, instead of sliding the ball across to Mauro Boselli, he clipped tamely at Andujar.
Lodi's second free-kick missed a post by a lick of paint on the half hour mark and Ilicic tested Andujar's responses at the other end with a fierce strike from distance.
Andujar got low to block a Jasmin Kurtic daisy-cutter with time running out and Giuseppe Bellusci did enough to distract Boselli as he tried to convert an Ilicic cross.
It was time for Sorrentino to look lively as play resumed, with yet another Lodi set-piece sailing dangerously close to his near post.
The former Chievo keeper punched a sliding Gonzalo Bergessio effort clear in the 51st minute and it was not long before he had to repel a Lucas Castro shot on the turn.
It seemed Sorrentino had weathered the storm but the 69th minute brought a goal that threatened Palermo's top flight status.
Barrientos would hurt the north coast outfit with a deflected shot from Alejandro Gomez's cross that skipped beyond a helpless Sorrentino.
Catania were not satisfied and plundered forward at will during the final 10 minutes.
After Sorrentino palmed a dipping drive from Bergessio to safety, the Elefanti watched helplessly as defender Nicola Legrottaglie failed to tuck home Castro's cross to the far post.
That miss would haunt the hosts and prove priceless to their rivals as Ilicic forced the draw with the last kick of the game.
Four minutes into stoppage time, the mercurial midfielder swept up Abel Hernandez's pass to beat Andujar with his left foot.
The goal inspired jubilation in the away end and a scuffle on the pitch, with Catania's Argentinian keeper seeing red for his role in the proceedings.