The breakthrough in Friday night's game came on 24 minutes after a sustained period of pressure from the hosts, with Jovetic rifling into the bottom-right corner from the edge of the area for his first goal in Ligue 1.
Fellow new arrival Ghezzal also opened his account as he arrived unmarked at the back post on the half-hour mark to fire Almamy Toure's delivery beyond Mike Maignan.
Lille were barely given a chance to mount a comeback after the restart as Falcao made sure of the points in the 48th minute, nodding home a rebound following Maignan's save from Rony Lopes.
The rout was completed in the 73rd minute when Rominigue Kouame clipped the heels of Jorge in the box to gift Leonardo Jardim's charges a penalty, which Falcao confidently put away from 12 yards.
Monaco sit second in the Ligue 1 table, with PSG's game in hand taking place on Saturday afternoon at Montpellier.