The French champions, who still lead the standings with 15 points from seven games, looked nothing like the team who crushed Real Madrid 3-0 in the Champions League last week, failing to create clear chances at the Parc des Princes.
Hassane Kamara headed home in the first half and Boulaye Dia doubled the tally with a bicycle kick in added time to give the visitors a deserved victory.
Reims are eighth on 11 points.
Earlier, Victor Osimhen scored his sixth league goal of the season to inspire Lille to a 2-0 home win over Racing Strasbourg.
The 20-year-old Nigerian opened the scoring and Loic Remy doubled the lead as the side from northern France moved up to third in the standings on 13 points.
Angers are second, behind PSG on goal difference, after Rachid Alioui’s late double gave them a 2-0 win at Toulouse.
Olympique Lyonnais extended their winless streak to six games in all competitions as goals by Maxwel Cornet and Moussa Dembele were cancelled out by Yoann Court’s double in a 2-2 draw at Stade Brestois.
Lille will take on Chelsea in the Champions League next week when Lyon, who are 11th in Ligue 1 on nine points, travel to RB Leipzig.
With Idrissa Gueye rested, Marco Verratti suspended and Marquinhos starting on the bench, PSG, already without injured strikers Kylian Mbappe and Edinson Cavani, struggled at the Parc des Princes, especially in midfield.
Kamara put the visitors ahead on 29 minutes as he headed home from Marshall Munetsi’s cross with his team’s first effort on target.
Eric Choupo-Moting was replaced by Angel Di Maria shortly before the interval after colliding with Neymar but that did little to lift the hosts.
It was Reims who threatened, but Oudin’s crossed shot from inside the area hit Keylor Navas’s right-hand post in the 78th minute.
Thomas Tuchel’s side were unable to create danger in the closing stages and were effectively handed their first home defeat in Ligue 1 since they lost to Rennes 2-0 at the Parc in May 2018, when Dia’s strike four minutes into stoppage time sealed victory for Reims.