Reims were reduced to ten men on 15 minutes when Pape Souare was given his marching orders for injuring Jonathan Pitroipa with a dreadful challenge.
The hosts made their numerical advantage count, dominating the first period and coming again on 30 minutes when Romain Alessandrini's shot from the edge of the box called Agassa Kossi into action.
They took a deserved lead just before half-time. Alessandrini provided a pinpoint cross and Erding nodded into the bottom corner from six yards.
Both sides has chances in the second period, with Antoine Devaux and Kamel Ghilas coming close for the visitors and Alessandrini striking the post at the other end, but Erding's first-half header proved the decider.