Tom Wilson and John Carlson each had a goal and an assist for the Capitals (12-9-2), who were coming off a 5-3 loss against the Tampa Bay Lightning on Saturday but have won four of five. Justin Sourdif had two assists, and Logan Thompson made 22 saves.
Denton Mateychuk scored for the Blue Jackets (11-9-3), who have lost three of four (1-2-1). Elvis Merzlikins made 26 saves.
Chychrun gave the Capitals a 1-0 lead a 6:05 of the first period. Ryan Leonard had the puck poked away from him in the high slot, but Chychrun pick it up, skated into the left circle and beat Merzlikens blocker side with a snap shot.
Wilson made it 2-0 at 16:29 of the second period. Sourdif skated down the ride wing and dropped a pass in the bottom of the circle to Aliaksei Protas, who quickly fed it across to Wilson for a one-timer into an open net.
Chychrun increased the lead to 3-0 with 15 seconds remaining in the period, scoring a power-play goal with a shot from the point.
Carlson then scored with three seconds remaining in the period to make it 4-0. Sourdif won a face-off in the right circle back to Alex Ovechkin, who swept the puck across to Carlson for a one-timer from the high slot.
Martin Fehervary made it 5-0 at 4:05 of the third period, scoring on a one-timer from the right point.
Mateychuk made it 5-1 at 5:50 when he scored on a rebound from the right circle.
Columbus forward Mathieu Olivier left the game late in the first period with an upper-body injury, and defenseman Zach Werenski left late in the second period with an upper-body injury. The Blue Jackets were already playing without forward Kirill Marchenko, who left the morning skate with an upper-body injury.