Adam's seventh goal of the year midway through the first quarter broke a scoreless tie and put the Sabres ahead to stay, and his second 1 minute into the final frame gave Buffalo a 4-1 lead.
Enroth stopped all 12 shots he faced in the third period and improved to 7-3-0.
Jason Chimera scored on a penalty shot for the Capitals' only goal.
Tomas Vokoun turned aside 23-of-28 shots as Washington dropped a fourth straight road game.
Celebrity Couples of 2014 [PHOTOS]