Faulk and Riley Nash each had a goal and an assist for Carolina, which had won four straight. Khudobin made 35 saves.
Staal pulled Carolina within 3-2 when he converted a pass from Jeff Skinner at 8:38 of the third period. Faulk tied it with a wrist shot from the left point that eluded Peters with 6:07 left in regulation.
Peters, drafted by Carolina in 2004, played in 68 games for the Hurricanes from 2009-14. He signed with Washington in July.
The Hurricanes trailed 2-1 after one period despite being outshot 18-3. Khudobin made several point-blank saves as the Capitals repeatedly swarmed the Carolina zone.
Washington broke through on a power play at 7:26 when Brouwer's shot deflected into the air. Carolina's Patrick Dwyer attempted to swat the puck out of danger, but instead sent it past Khudobin.
The Capitals made it 2-0 when Beagle fielded Carlson's shot off the back wall and banked the puck in off Khudobin for his first point of the season.
Carolina made it 2-1 with a power play goal by Nash, who beat Peters high on a drive from the left circle with 49 seconds left.
Fehr made it 3-1 at 16:48 of the second period when he broke in on Khudobin, deked, and slid the puck toward the net and had it deflect in off Carolina's Brett Bellemore.
NOTES: Ovechkin ranks second on the Capitals' franchise assists list behind Michal Pivonka (418). ... Carolina D Tim Gleason missed his second straight game with an upper-body injury. ... Washington C Brooks Laich sat out and is day to day with an upper-body injury. He had returned to the lineup Friday in Chicago after missing seven games. ... Capitals RW Tom Wilson left the game in the second period with a lower-body injury.