Teenager Hervin Ongenda equalised eight minutes from time in his first competitive game for PSG as a substitute to cancel out Henri Saivet's 38th-minute opener in the Trophee des champions.
Paris St Germain, whose new coach Laurent Blanc has vowed to win all the domestic trophies this season, was left frustrated for most of the match by a well-organised Bordeaux side.
"It had been a very difficult game and it shows that all the teams who will face PSG will be extremely motivated," Blanc told French broadcaster beIN Sport.
"We're not fully ready because some players have joined the squad late," added former France captain Blanc, whose side visit Montpellier in the Ligue 1 curtain raiser next Friday.
The Qatari-backed Paris club were without recent signings Uruguay striker Edinson Cavani and 19-year-old Brazilian defender Marquinhos, who were left in France to train.
PSG dominated possession and Ezequiel Lavezzi, paired with Zlatan Ibrahimovic up front, went close to opening the scoring after 13 minutes when he picked up a loose ball and ran at goal only to be denied by Bordeaux keeper Cedric Carrasso.
The capital club continued to push hard but they conceded the opener when Saivet headed home a Nicolas Maurice-Belay cross from the left following a quick counter-attack.
Gabon-born Andre Poko, cheered on by the crowd throughout the game, failed to make it 2-0 for Bordeaux near the hour mark when he lost out in a one-on-one with Salvatore Sirigu.
It was the last chance for the Cup winners to take a firm grip on the game as Ibrahimovic, although denied a goal in the 79th minute for offside, superbly set up Ongenda to equalise before Alex's winning header in the fourth minute of added time.
(Reporting by Gregory Blachier; Editing by Ken Ferris)
