Christophe Galtier’s men eased to a straightforward win, with Portuguese centre-back Xeka and the in-form Jonathan David both finding the net.
Lille, who lead Paris Saint-Germain by two points in the Ligue 1 title race, are bidding for a first major trophy since winning the league and cup double in 2011.
They kept their hopes of repeating that feat alive on Sunday despite naming a much-changed side.
Gazelec played in Ligue 1 in the 2015-16 season but have been relegated three times since.
But they did themselves no favours in their attempt to cause an upset, as Alexandre Durimel gave Lille the perfect start with a ninth-minute own goal.
The hosts stayed in the game until late on, but Xeka struck in the 73rd minute and Canadian international David, on as a substitute, scored his eighth goal in 13 games 11 minutes later.
Gazelec did manage to grab a consolation through David Pollet with three minutes remaining.
Elsewhere, Martinique club Franciscain’s run came to an end as they were thrashed 5-0 by Ligue 1 club Angers.
Chateaubriant booked a last-16 spot with a 2-1 win at fellow fourth-division club Romorantin.
Later on Sunday, Marseille play their final match before Jorge Sampaoli takes over as coach when they visit fourth-tier Chanet.
On Saturday, holders Paris Saint-Germain eased through with a 3-0 victory at Brest, while Lyon beat second-tier Sochaux 5-2.
Red Star, five-time winners of the competition now languishing in the French third tier, struck twice in the last seven minutes to eliminate top-flight Lens 3-2.