Hassane Kamara headed in the first-half opener for Reims, who clinched victory with an acrobatic volley from Boulaye Dia that crept inside the post in second-half stoppage time.
A second league loss of the season ended a four-match winning streak for PSG, who stayed top of Ligue 1 after seven games but were joined on 15 points by Angers after their 2-0 win at Toulouse.
Already missing Edinson Cavani and Kylian Mbappe, PSG lost another striker to injury when Eric-Maxim Choupo-Moting went off late in the first half. PSG coach Thomas Tuchel paid the price for heavily rotating his lineup against a mid-table opponent.
Rachid Alioui scored from a free kick in the 88th minute and then again in the fifth minute of stoppage time for Angers, who are the surprise of the season in France.
Lille are in third place, two points behind the top two, after winning 2-0 at home to Strasbourg. Nantes remained tied on points with Lille thanks to a 1-0 home win over Rennes, the other side to beat PSG this season. (AFP)