Marseille, without silverware since their 1993 Champions League triumph, floored the Ligue 1 champions with three second-half goals at the Stade de France.
Defender Souleymane Diawara and substitute Mathieu Valbuena put them 2-0 up before Bordeaux defender Mathieu Chalme deflected a Valbuena free kick into his own net.
Bordeaux defender Ludovic Sane then headed a late consolation goal in the 85th minute.
Sane's team, trying to win the League Cup for a record fourth time and hoping for a boost before visiting Olympique Lyon in the first leg of their Champions League quarter-final on Tuesday, struggled in a tense, tactical affair.
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Diawara showed Marseille the way when he headed home a Lucho Gonzalez corner on 61 minutes. Midfielder Valbuena doubled the advantage six minutes later, collecting a fine pass by forward Hatem Ben Arfa to fire home.
With his team 2-0 down, Bordeaux coach Laurent Blanc switched his focus to the Lyon game and substituted arguably his best two players, France playmaker Yoann Gourcuff and Morocco striker Marouane Chamakh.
The match was rough and marred by a few ugly scenes, notably a nasty tackle on Lucho from Sane who escaped with a booking.
YELLOW CARDS
By the 15th minute referee Stephane Lannoy had already shown three yellow cards.
The first clear chance was for Bordeaux on 22 minutes, a low drive from Gourcuff.
The best opportunity before the break fell to Marseille when a curling shot from just inside the box by Brazilian forward Brandao was well punched out by keeper Ulrich Rame.
With their fans making a lot more noise than the Bordeaux supporters, Marseille stepped up a gear in the second half, showing more initiative and proving the better side.
Marseille came close to ending their trophy wait when they lost French Cup finals in 2006 and 2007 and the UEFA Cup finals of 1999 and 2004.
The team from the football-mad Mediterranean port city were also stripped of the 1993 French title and demoted to the second division over a bribery scandal.
Saturday's win was a relief for their fans and also set the scene for a thrilling Ligue 1 finale, with Marseille just three points behind Bordeaux.
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