Substitute Kadewere cancelled out Mathieu Cafaro's first-half opener two minutes into stoppage time to put third-placed Lyon on 60 points from 29 games behind Paris Saint-Germain on goal difference and two off league leaders Lille.
PSG welcome Nantes and Lille travel to Monaco on Sunday.
Lyon, who extended their unbeaten run away from home to 13 games, will see fourth-placed Monaco move within two points of them if the principality side win on Sunday.
In Reims, the hosts deservedly broke the deadlock after 33 minutes when Cafaro unleashed a fine half-volley that flew under the crossbar.
Reims, who are 11th on 35 points, had another great chance through Cafaro but Anthony Lopes's save kept Lyon afloat.
The visitors were eventually rewarded when Kadewere headed home from Memphis Depay's cross to salvage a point.