Striker Roux unleashed a low cross-shot in the 117th minute as Lille joined St Etienne, Troyes and Stade Rennes into the last eight of the competition.
Lille dominated throughout but were kept in check by a stern Toulouse defence, who looked more vulnerable after Steeve Yago was sent off after picking up a second yellow card in the 86th minute.
Toulouse keeper Olivier Blondel kept his team afloat with superb saves to deny Marvin Martin and Roux but was powerless when Martin set up Roux for a deserved winner from just on the edge of the box.
Earlier, a Romain Hamouma double inspired St Etienne to a 3-0 win at Sochaux.
Ligue 2 leaders Monaco took the lead at home against Troyes thanks to a Yannick Ferreira Carrasco penalty but the principality side lost control after the break with Rincon and Quentin Othon scoring for the visitors.
Rennes needed just one goal from Romain Alessandrini in the first half to see off Ligue 2 strugglers Arles-Avignon.
Holders Marseille take on fierce rivals Paris St Germain on Wednesday, while Lyon travel to Nice, Montpellier host Bordeaux and Bastia welcome Auxerre, the last Ligue 2 side in the competition.