Montpellier, second in the Ligue 1 standings, were also knocked out following a 2-1 home defeat to Lorient thanks to Costa Rica striker Joel Campbell, who struck in the 68th after Olivier Giroud had cancelled out Innocent Emeghara's first-half opener for the visitors.
French champions Lille made light work of Ligue 2 side Sedan, goals by Benoit Pedretti, Joe Cole and Ireneusz Jelen giving them a 3-1 home victory.
The Saint-Etienne v Olympique Lyon game ended in a 2-1 win for the visitors at their arch-rivals, but the match was halted after fans threw flares onto the pitch when a penalty was awarded to Lyon.
Referee Clement Turpin sent the players back to the dressing room but play resumed after a five-minute interruption and Michel Bastos converted the penalty to add to Jimmy Briand's first-half opener.
Pierre-Emerick Aubameyang fired home from 20 metres eight minutes from time to reduce the arrears.
Stade Rennes were knocked out 4-1 on penalties by Ligue 2 Le Mans after the game had ended 0-0.
In Dijon, PSG started without playmaker Javier Pastore, midfielder Nene and striker Kevin Gameiro, but opened up a 2-0 lead after 20 minutes before collapsing.
The 18-year-old winger Jean-Christophe Bahebeck put the visitors ahead in the 16th minute with a fine, curled free kick and Turkey striker Mevlut Erding doubled the tally four minutes later from a Jeremy Menez cross.
But Dijon, who were promoted this season, netted two goals in the space of three minutes before the break to level.
Uruguay defender Diego Lugano fouled striker Brice Jovial in the box and Younousse Sankhare converted the penalty. Then Florin Berenguer equalised from close range after connecting with a Jovial cross.
The hosts went ahead shortly after the hour when Jovial netted from the spot after Zoumana Camara had handled the ball in the area.
PSG coach Antoine Kombouare replaced Mathieu Bodmer and Erding with Nene and Gameiro 20 minutes from time but although the visitors hit the woodwork twice, Dijon held on.
On Tuesday, holders Olympique Marseille crushed Ligue 2 side RC Lens 4-0 to advance to the quarter-finals.
