The Blue Jackets led 3-0 after the first period.
"We just gave up those early goals, which puts us in a hole, and then the game's essentially decided at that point," Capitals coach Spencer Carbery said. "So, then it becomes what it was. You just get through the periods."
Hunter Shepard allowed seven goals on 26 shots for the Capitals (50-20-9) in his season debut.
Forward Alex Ovechkin, who set the NHL all-time goals record last Sunday, and defenseman Jakob Chychrun each did not play due to rest. Washington previously clinched the Metropolitan Division and No. 1 seed in the East.
Carbery said after the game Ovechkin would play in the home game against the Blue Jackets on Sunday, although he was unsure about Chychrun.
"Obviously, the stakes are different for both teams," Capitals forward Nic Dowd said. "But it doesn't matter. I think if we play our game and play with detail and work hard, I think good things are going to happen."
Zach Werenski made it 1-0 at 1:00 of the first period from the left face-off dot. His 21st goal set the Blue Jackets record for most goals by a defenseman in a season.
Johnson upped the lead to 2-0 at 4:45 scoring in front.