Edinson Cavani had scored in the 24th minute to raise hopes that Laurent Blanc's side could clinch their second successive Ligue 1 title on their visit to third-from bottom Sochaux.
"We didn't deserve to win this game, we didn't play as (well as we) usually do," said Paris St Germain president Nasser al Khelaifi. "We must clinch title at home."
Sochaux's own hopes for staying up next season were boosted by the result.
Dimitar Berbatov's double strike on Saturday helped second-placed Monaco crush bottom club Ajaccio 4-1 to keep the title race alive.
PSG, who won the French League Cup by beating Olympique Lyon 2-1 last weekend, have 83 points with three games remaining. Monaco are eight points adrift.
In the day's other games, Lille strengthened their hold on third spot with a 2-1 win over Bordeaux, while Lyon thumped Bastia 4-1.
- Sports & Recreation
- Laurent Blanc
- Edinson Cavani
- Dimitar Berbatov