The Slovenian forward put the visitors ahead on the half-hour after skipping between two defenders in the box and firing through another's legs to wrongfoot goalkeeper Lorenzo Montipo.
Ilicic was close to adding a second with an explosive shot that crashed off the post but his good work was undone when the unmarked Marco Sau tapped in a cross to equalise for the hosts against the run of play early in the second half.
However more Ilicic magic soon helped Atalanta back in front in the 69th minute as he played a one-two on the edge of the area with Cristian Romero before striking a shot that Montipo could only parry into the path of Rafael Toloi for a tap-in.
Two minutes later Atalanta took control when Ilicic curled an inviting cross to the back post where Duvan Zapata was on hand to volley home and substitute Luis Muriel completed the rout by curling in his 10th league goal of the season late on.
The result stretched Atalanta's unbeaten league run to seven matches and leaves them fourth on 31 points ahead of the rest of the weekend's fixtures. Benevento remain 10th on 21 points.