PSG host relegation battling Le Havre on Saturday
Roberto Mancini's side had been frustrated by Turkey's defensive approach in the first half but broke through in the 53rd minute when a hard-hit cross from Domenico Berardi flew in off Turkey defender Merih Demiral for an own goal.
Insigne made it 3-0 in the 79th minute with a confident, curling finish after some sloppy defending from the disappointing Turks.