A late goal from Cedric Kante gave Nice a 1-0 win over bottom Ligue 1 club Le Havre on Tuesday and a place in the French League Cup semi-finals.
Defender Kante volleyed home from a corner two minutes from time to snatch victory for Nice, the losing finalists in 2006 and currently eighth in the Ligue 1 standings.
The French Riviera side next meet Vannes, who knocked out Ligue 2 rivals Metz in Tuesday's other quarter-final tie, winning 4-3 on penalties after the sides were tied 1-1 after 90 minutes and extra time.
The last two quarter-finals are on Wednesday with Girondins Bordeaux welcoming second division Chateauroux and holders Paris St Germain hosting second division Racing Lens in a rematch of last year's controversial final.
Some PSG fans held up an abusive banner aimed at their visitors during the 2008 title match, won 2-1 by the Paris side last March at the Stade de France.
The French League initially banned PSG from this year's edition but a civil court later quashed that decision and the two sides will meet again, this time at Parc des Princes.