Bordeaux looked to have claimed a surprise win after Henri Saivet had given them the lead, but late goals from Hervin Ongenda and Alex - the latter in the fifth minute of injury time - earned the Ligue 1 champions their first silverware of the new season in a game played in Gabon.
Zlatan Ibrahimovic remained the focal point of the PSG attack, with new signing Edinson Cavani left out of the squad, while former Chelsea defender Alex was favoured over Mamadou Sakho to partner Thiago Silva in the centre of defence.
Bordeaux coach Francis Gillot selected Saivet to lead the line, with Maxime Poundje - who recently signed a new contract with the club - starting at left-back following the departure of Benoit Tremoulinas.
Laurent Blanc's men made the better start to proceedings and forced the first chance of the game as goalkeeper Cedric Carrasso prevented Ezequiel Lavezzi from opening the scoring after the Argentine had capitalised on an error from the Bordeaux defence.
PSG continued to force the issue, and they saw another chance go begging as Thiago Silva glanced a header wide from a Thiago Motta free-kick.
The Coupe de France winners did eventually manage to gain a foothold in the game and they took a surprise lead after 38 minutes - Saivet evading the PSG defence to head home Nicolas Maurice-Belay's left-wing cross at the near post.
Gillot's charges then held on until the break with little difficulty and it was they who created the better chances at the start of the second half, with Maurice-Belay cutting in from the left only to see his fierce, low effort fly wide of the far post.
Bordeaux continued to frustrate PSG, and their lead should have doubled their lead when Gabon international Andre Biyogo Poko was denied a memorable goal in his homeland, as Salvatore Sirigu produced a fine save to halt a determined solo run from the 20-year-old.
Searching for a spark to ignite his side, Blanc opted to shuffle his pack, making three changes in the space of five minutes as Marco Verratti, Kingsley Coman and Hervin Ongenda replaced Javier Pastore, Motta and Lavezzi.
PSG thought they had levelled after 78 minutes, with Ibrahimovic heading in Christophe Jallet's far-post cross, but the assistant referee incorrectly disallowed the goal for offside.
That incident proved to be inconsequential, though, as PSG found the equaliser in spectacular fashion three minutes later when Ongenda netted with a sublime first-time finish after latching on to a superb lofted pass from Ibrahimovic.
The contest looked to be heading for a penalty shoot-out as a fatigued Bordeaux clung on in the closing stages, but their resolve was finally broken in heartbreaking fashion in the fifth minute of added time, Alex meeting Lucas Moura's free-kick to direct a powerful header into the bottom corner and snatch a winner.