Questions are once again likely to be raised regarding Laurent Blanc's future at the club, with the Ligue 1 champions' performance doing little to dispel suggestions that the coach has lost the dressing room.
Blanc has found himself coming under increasing pressure after presiding over an underwhelming title defence so far, although his side were lively in the first half against his former club.
Edinson Cavani, the subject of intense transfer speculation, headed PSG into a 14th-minute lead at Parc des Princes as the hosts started confidently, with Javier Pastore doubling the lead just after the half-hour mark.
But Willy Sagnol's side produced a marked improvement after the break and pulled one back through Diego Rolan, who became something of a nuisance.
Bordeaux's chances of completing the comeback were helped by Zoumana Camara's red card for a second booking in the 83rd minute, but PSG ultimately claimed victory to secure a place in the last 16.
PSG looked dangerous during the opening stages as they floated a series of teasing crosses into the penalty area, with Thiago Silva spurning the first chance of the game as he headed wide from one of them in the 12th minute.
There was no such let-off for Bordeaux a minute later, though.
The visitors again failed to cope with a cross, this time courtesy of Lucas Digne, who produced a fine delivery from the left and Cavani confidently nodded in after getting in front of Cedric Yambere.
Bordeaux almost drew level in the 26th minute, but Yambere saw his effort crucially blocked by Adrien Rabiot.
PSG soon made the most of that escape too, as they doubled their lead six minutes later - Pastore this time tapping in after goalkeeper Cedric Carrasso could only parry Ezequiel Lavezzi's first-time effort.
Blanc's side showed no signs of letting Bordeaux off the hook after getting the second, as Lavezzi twice tested Carrasso in the lead up to half-time.
It did not take long for Bordeaux to restore parity after the break, though, as Rolan pounced on a loose ball and calmly stroked into the bottom-left corner less than a minute after the restart.
The Uruguayan forward continued to pose a threat for Bordeaux and he tried his luck again six minutes later, but blazed well over from 20 yards after a penetrating move down the right.
Any fluidity in PSG's game had seemingly vanished at half-time, with the home side appearing bereft of ideas in the final third.
And a rash challenge on Enzo Crivelli from Camara earned the centre-back his second yellow card of the night, but Bordeaux were unable to capitalise on their numerical advantage, as PSG held on to the slender win.
