Paris-Saint Germain and Bastia progressed to the Coupe de la Ligue semi-finals by beating Saint-Etienne and Rennes respectively on Tuesday.
Laurent Blanc had called for a response from his PSG side after they threw away a two-goal lead to lose 4-2 at Bastia in Ligue 1 on Saturday, and Zlatan Ibrahimovic's goal 18 minutes from time at Stade Geoffroy-Guichard was enough to see them through 1-0.
The French champions have picked up just one point from their last three league matches and are down in fourth place, but Ibrahimovic's chested finish gave them a morale-boosting victory.
There was drama after the only goal of the game as play was suspended by referee Said Ennjimi as a result of objects being thrown onto the pitch by the home supporters.
When the game resumed the Coupe de la Ligue holders were grateful for goalkeeper Nicolas Douchez, who produced an outstanding reflex save to keep out Ricky van Wolfswinkel's late header.
Defeat for Saint-Etienne, who moved above PSG into third spot in Ligue 1 at the weekend, was only their second in 18 matches and their first at home since October.
In-form Bastia have now won five of their last six games in all competitions after they beat nine-man Rennes 3-1 at Stade Armand Cesari.
Sylvain Armand put the visitors in front, but Bastia, buoyed by their stunning win over PSG, fought back to advance courtesy of a Sebastien Squillaci strike, Romain Danze's own goal and Djibril Cisse's late goal.
Rennes had Anders Konradsen and debutant Ermir Lenjani sent off in the second half as their opening goal proved to be a false dawn.
Monaco host Guingamp and Nantes travel to Lille in the other two quarter-finals on Wednesday.