Dijon held out for 47 seconds before Wesley Lautoa scored an own goal, though Mounir Chouiar did equalise.
Edinson Cavani had a goal ruled out by VAR but Kylian Mbappe lashed home and Thiago Silva headed in an exceedingly third.
Pablo Sarabia scored from two Mbappe crosses and Senou Coulibaly scored another own goal during a thumping finale.
PSG, without forward Neymar as he recovers from a rib injury, lost last year’s final on penalties to Rennes but won the four previous titles and are again within striking distance of the trophy.
Rennes reached the last four with a 3-0 win at fourth division side ASM Belfort on Tuesday, while Lyon host Marseille afterward Wednesday.