The French champions, who lost to Olympique Lyon in the quarter-finals of European club football's premier event with a 3-2 defeat on aggregate on Wednesday, remain fifth in the standings with 56 points from 30 games.
Bordeaux stay three points behind leaders Olympique Marseille, who have also played 30 games and host lowly Nice on Sunday.
The turning point in the match in Paris came on the half-hour when Bordeaux goalkeeper Ulrich Rame was sent of for handling the ball outside his area.
Defender Sylvain Armand converted the resulting free-kick, which was deflected and gave 19-year-old substitute Bordeaux keeper Abdoulaye Keita no chance.
Turkey striker Mevlut Erding fired home under the bar to double PSG's advantage after 75 minutes.
Bordeaux pulled one back with a headed goal by defender Ludovic Sane five minutes from time but forward Guillaume Hoarau sealed the home side's win, also with a header.
"Defensively we're just not good enough to reach our goals," Bordeaux defender and captain Marc Planus told French television channel Orange Sport. "It's a pity because we have good players up front but at the back we're simply not at the same level."
INCIDENT-PACKED DRAW
Surprise package Montpellier moved up to second place with an incident-packed 2-2 draw at Le Mans while Grenoble's slim hopes of remaining in the top flight came to an abrupt end.
Grenoble's 4-0 defeat at Toulouse combined with St Etienne's 2-0 win at Sochaux left the bottom club 20 points from the safety zone with 18 points left to play for.
"We're officially in Ligue 2 but we've known for a while we would be," Grenoble coach Mehmed Bazdarevic told reporters. "We had been fighting hard lately but tonight we made it easy for Toulouse."
Montpellier moved onto 58 points from 32 games, one point behind Marseille.
Belgium striker Roland Lamah put Le Mans ahead with the fastest goal in Ligue 1 this season after 17 seconds and gave the home side a share of the points 20 minutes from time.
Midfielder Karim Ait-Fana had levelled for Montpellier and forward Souleymane Camara put them 2-1 ahead with a penalty after 34 minutes.
A fight broke out on the pitch late in the first half and Montpellier midfielder Cyril Jeunechamp was sent off along with Le Mans's Gregory Cerdan, who left the substitutes bench to get involved.
Olympique Lyon and Auxerre, in third and fourth two points off the pace, host Lille and visit Nancy respectively on Sunday.
