Modeste struck eight minutes from time to send his club, who won promotion to Ligue 1 this year, into the last eight at the expense of the fallen giants who currently reside in the second tier.
Their reward is a home tie against Lille, who were thumped 6-1 in the Champions League the same evening by the Bungesliga's Bayern Munich at the Allianz Arena.
Ligue 1 champions Montpellier host Nice while Paris St Germain travel to Saint Etienne, who defeated the big spenders at Parc des Princes in the league at the weekend.
In the fourth quarter-final of the draw, Rennes were handed a home tie against Troyes.
Coupe de la Ligue quarter-final draw:
Montpellier v Nice
Bastia v Lille
St Etienne v Paris St Germain
Stade Rennes v Troyes
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