Both teams came into the game having lost two in a row and the Capitals failed to make up ground in their bid to catch Winnipeg for the final playoff berth in the Eastern Conference. The idle Jets maintained a three-point lead over Washington.
Washington lost a two-goal lead, fell behind by one and tied it on a goal by Brooks Laich with 2:52 left in regulation.
Faulk then beat Michal Neuvirth with a wrist shot to bring Carolina its 24th win of the season. Only Columbus, with 21, has fewer victories in the league.
Cam Ward made 46 saves for Carolina. Neuvirth stopped 32 shots.