Reims midfielder Grzegorz Krychowiak struck the only goal of the game from the penalty spot as Lyon slumped to a third consecutive Ligue 1 defeat on Sunday.
Lyon, who are now winless in five matches, had to play for the final 39 minutes with 10 men after Milan Bisevac was shown a straight red card for a professional foul on Diego.
Krychowiak powerfully dispatched the resultant spot kick into the centre of Remi Vercoutre's net.
Reim, who extended their unbeaten home run to five games, are now four points clear of the relegation zone, while Lyon remain fourth.
