Nancy's Yohan Mollo (pictured) struck a minute from time after Mohamed Sissoko had cancelled out Bakaye Traore's first-half opener as PSG stayed second with 60 points from 30 games.
They trail Montpellier on goal difference after the leaders' game at Olympique Marseille was put back to April 11.
Nancy midfielder Traore raced into the PSG central defence to beat Salvatore Sirigu from close range after 18 minutes.
The visitors dominated possession but failed to find the target before the break and eventually suffered their first league defeat in four months.
Sissoko equalised five minutes into the second half with a header from a Sylvain Armand cross and although Carlo Ancelotti's side piled on the pressure, Nancy held on.
They claimed all three points when Mollo beat Sirigu from the edge of the box after Maxwell lost the ball in the midfield.
MAJOR BLOW
Saint-Etienne's Champions League hopes suffered a major blow when they lost their third league game in a row, a 3-2 home defeat by struggling Nice.
Anthony Mounier struck twice for the visitors and Francois Clerc poked home the winner a minute from time as Saint-Etienne stayed sixth with 46 points from 30 games. Nice are sixth from bottom on 31 points.
The top two qualify for next season's Champions League and the third-placed side go through to a play-off tie.
Saint-Etienne went ahead in the 22nd minute when Max Gradel unleashed a 30-metre piledriver, only for Nice to equalise through Mounier in the 34th.
Les Verts restored their advantage thanks to a Sylvain Marchal header before the break but the unmarked Mounier levelled 11 minutes into the second half with a diving header.
Former France full-back Clerc then sealed the win when he converted a pass from Renato Civelli.
Girondins Bordeaux drew 1-1 at home to Dijon remain in eighth place on 42 points.
Benoit Tremoulinas opened the scoring with a penalty in the 71st minute but Thomas Guerbert snatched a point for the visitors in stoppage time.
Sochaux claimed a 2-1 comeback win at home to Stade Brest in a relegation battle while bottom club Auxerre also boosted their chances of avoiding the drop by beating Valenciennes 2-0.
Sochaux are third from bottom on 30 points behind Brest on goal difference with Auxerre three points from the safety zone.
