Olivier Dall'Oglio's side controlled the contest and were two goals ahead by half-time thanks to Julio Tavares and Florent Mollet.
The latter went on to complete a hat-trick in the second half, while Romain Philippoteaux and Brian Babit also found the back of the net.
The hosts pulled one back after 74 minutes, but it was nothing more than a consolation as Dijon comfortably progressed.
Third-tier Quevilly - runners-up in 2012 - were given much more of a scare against Saint-Louisienne after going behind in the 22nd minute, but Joris Colinet levelled and the match went into extra time.
Grenoble and Yzeure join them in the next round after victories over Pezenas and Illkirch Graffenstaden respectively, although the former needed extra time to record their 2-1 win.
Sedan surrendered a one-goal lead to lose 2-1 against Pagny Sur Moselle, while Sarre Union beat Fleury-Merogis, who had a man sent off, 1-0 after extra time.
Amiens survived extra-time as two late strikes secured a 3-1 win over Meaux Academy, and Consolat Marseille needed penalties to book their spot at the expense of Martigues, who finished the match a man down.
Sunday also saw wins for Red Star, Saint-Omer and Iris Club de Croix, all three sides triumphing away from home in normal time.
