The home side tried to put Chievo under pressure in the opening stages as Alberto Gilardino burst forward just a couple of minutes after kickoff, but his effort was blocked, while Ilicic fired wide moments later.
Fiorentina broke the deadlock less than 15 minutes in when Mohamed Salah burst forward before crossing into the box for Ilicic to slot into the bottom corner.
Cristiano Biraghi tried to set up an equaliser down the other end, racing forward to beat the last defender, who recovered in time to turn the ball behind for a corner, but a foul on the keeper as the ball was played in let Fiorentina off.
Ilicic could have added a second midway through the period when Dario Dainelli gave away a free kick, which also forced Salah off injured, just outside the box, but the goalscorer's effort direct from the set piece was a fraction high.
Ruben Botta tried to create some pressure down the other end shortly before the interval, providing a couple of promising-looking balls into the box, but his teammates were unable to convert. body check tags ::