Grenoble came from behind three times to force a shootout in the third round tie and after each side converted their opening three penalties, Marseille winger Florian Thauvin saw his spot-kick tipped over the bar by Paul Cattier in the pivotal moment of the contest.
Fabien Tchenkoua then scored for Grenoble, Gilbert Imbula responded for Marseille and then Mourad Nasrallah struck the winning penalty for the hosts.
Andre Ayew had seemingly scored the decisive goal for Marseille in the eighth minute of extra time but, with the last attack of the match, Grenoble equalised again when Aziz Tafer's right-wing cross picked out Selim Bengriba, who glanced a header past Brice Samba.
It was no more than Grenoble deserved as Olivier Saragaglia's side regularly opened up Marseille's defence at the Stade des Alpes only to be denied by Samba, who made just his second appearance of the campaign.
Marseille took the lead in the sixth and 33rd minutes of regulation through Andre-Pierre Gignac but Grenoble hit back each time thanks to goals from Nasrallah and Fares Hachi.
As the game wore on, the visitors missed a number of chances to claim victory within 90 minutes with Thauvin particularly wasteful.
In extra time, Ayew poked home a goal after Dimitri Payet fed Michy Batshuayi on the right side of the penalty area and the Belgian's cross picked out Marseille's Ghanaian attacker but Marcelo Bielsa's men would go home empty-handed after Bengriba's late heroics and Cattier's save.
It was a good day for the other club from France's second-largest city with Consolat Marseille upsetting former Ligue 1 club Ajaccio 3-0.
Ajaccio were relegated from the French top tier last season but remain a division above Consolat in the league pyramid, with the latter playing in the Championnat National, but the visitors had few answers at the Stade de la Martine.
Consolat led by two goals at half-time after Abdoul Diawara and Marek Karim Amiri got on the scoresheet in the first period, while David Gigliotti wrapped up the home team's win with an 80th-minute strike.
Holders Guingamp began their defence with a comfortable 3-0 victory at Dinan-Lehon with Claudio Beauvue scoring a brace to send his team into the round of 32.
Beauvue struck in the 51st and 64th minutes, while Jeremy Pied completed the triumph with 10 minutes left, with Grenoble's opponents from last season's final - Rennes - beginning their campaign with a 2-1 win at Dunkerque.
Fifth-tier club Cholet advanced on penalties, despite having Kevin Berdier sent off in the 55th minute, after their tie with fourth-tier Beauvais remained scoreless through 120 minutes.
Tiny club Pagny-sur-Moselle, who play in Lorraine's Division d'Honneur - part of the sixth tier of French football, failed to continue their fairytale run as they went down 3-1 to Yzeure.
Bordeaux claimed their third win of the season over Derby de la Garonne rivals Toulouse, prevailing 2-1 at home.
Willy Sagnol's side had already defeated Toulouse in the Coupe de la Ligue and Ligue 1 and made it three from three thanks to an early penalty from Thomas Toure and Abdou Traore's strike.
Lyon held off Lens' late push to triumph 3-2, Saint-Etienne needed extra time to defeat Nancy 1-0 and Monaco triumphed 2-0 over Nimes.
Ligue 1 cellar-dwellers Caen were eliminated in extra time by second-tier Dijon, who won 3-2, Metz came from behind to defeat Epinal 2-1 and Auxerre edged out Strasbourg 1-0.
