Marseille and Nigeria full back Taye Taiwo
Nigeria international left-back Taiwo rifled home with 10 minutes to play, settling a game that had been high on physical commitment but lacking in attacking inspiration from either side.
Montpellier, appearing in their first final since losing to Auxerre in the 1994 French Cup decider, succeeded in disturbing Marseille's rhythm but were unable to put the holders' defence under serious pressure.
Marseille's defeat of Bordeaux in last year's final was the catalyst for their first French league title since 1992 and they will now hope for a similar boost in the current title race, as they trail leaders Lille by a point with seven games remaining.
A rugged opening witnessed several crunching challenges and there was a seventh-minute setback for Marseille when holding midfielder Stephane Mbia had to be replaced by Charles Kabore after appearing to jar his knee.
The fans at Stade de France had to wait until the 20th minute to see either goalkeeper make a save, with long-serving former Montpellier captain Laurent Pionnier boxing away a Lucho Gonzalez free-kick.
Marseille's Steve Mandanda was the first goalkeeper to be seriously tested, however, as two minutes later he had to kick away a close-range effort from Jamel Saihi after a high ball was allowed to bounce in the OM area.
Mathieu Valbuena, operating in a loose, central position, was Marseille's most enterprising player throughout and he came within inches of breaking the deadlock in the 32nd minute when he shook the left-hand post with a half-volley.
Cyril Jeunechamp then tested Mandanda with a rising drive from distance, before Souleymane Diawara produced a finely timed challenge to halt the progress of marauding Montpellier forward Souleymane Camara.
Despite boisterous support from boths sets of fans, the game remained scrappy and low on technical quality in the second half.
Andre Ayew twice threatened with his head for the holders, first obliging Pionnier to make a save and then guiding the ball fractionally wide of the far post from Valbuena's inswinging corner.
With extra-time beckoning, Marseille finally made the breakthrough in the 80th minute.
Montpellier failed to clear the ball from a free-kick, allowing Taiwo to drive the ball home through a crowd of players with his weaker right foot and keep the League Cup trophy at Stade Velodrome for at least another year.
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