Chychrun skated around New Jersey forward Paul Cotter down the left side on the rush and batted his own rebound out of the air past Jake Allen from in tight.
Aliaksei Protas had two goals and an assist, and Alex Ovechkin had a goal and an assist for the Capitals (20-13-5), who had lost three straight (0-2-1) and six of seven (1-4-2). Logan Thompson made 35 saves.
Jesper Bratt scored twice, and Cody Glass had a goal for the Devils (20-16-2), who have lost three straight (0-2-1). Allen made 29 saves.
Dylan Strome appeared to give Washington a 1-0 lead at 11:58 of the first period when he scored on a rebound, but New Jersey challenged the zone entry and after a video review the play was ruled offside.
Protas put the Capitals up 1-0 with less than a second left in the first period. Ovechkin controlled a loose puck along the left wall and centered to Protas, who redirected the puck over Allen.
Bratt tied it 1-1 with a power-play goal at 4:56 of the second period. Nico Hischier got to a rebound in the slot and quickly passed to Bratt, who scored with a snap shot from the bottom of the right circle.
Anthony Beauvillier put the Capitals ahead 2-1 at 17:33. New Jersey forward Jack Hughes turned the puck over to Protas in the Devils' defensive zone, and then Beauvillier collected the loose puck and beat Allen with a wrist shot from the low slot.
Bratt evened the game 2-2 with his second goal at 7:00 of the third period when he spun around at the left point and scored on a wrist shot through a screen.
Glass gave the Devils a 3-2 lead just 32 seconds later at 7:32, beating Thompson's left skate with a tap-in from the bottom of the right circle off a pass from Connor Brown.
Ovechkin tied it 3-3 at 9:17. Rasmus Sandin skated down the slot and passed to Ovechkin at the left of the net, where he lifted a wrist shot over the stick of a sprawling Allen.
