The Ligue 1 leaders' attacking football was too much to handle for Nice and Lille prevailed through goals by Eden Hazard and Gervinho either side of the interval.
They will take on either Ligue 2 side Angers or Paris Saint-Germain, who play on Wednesday, in the final at the Stade de France on May 14.
Balmont's injury, however, was a blessing in disguise as it took his replacement Hazard only eight minutes to make an impact.
The Belgian prodigy, twice voted the league's top prospect, played a fine one-two with Ludovic Obraniak and unleashed a fierce shot from the edge of the box that went under the bar after taking a slight deflection off a Nice defender.
The hosts reacted, with Gabon striker Eric Mouloungui's header hitting Mickael Landreau's crossbar in the 56th minute, but Lille weathered the storm.
