Johnson won it when he finished a 2-on-0 rush with Adam Fantilli.
The goal came after Jamie Drysdale tied the game 3-3 for the Flyers with 11 seconds remaining in the third period. With Dan Vladar pulled for an extra attacker, Drysdale got to the front of the net, and Tyson Foerster's centering pass went off his skate and in.
Johnson also had an assist, while Fantilli added a goal for Columbus (5-5-0). Denton Mateychuk scored and Cam Talbot made 28 saves.
Trevor Zegras had a goal and an assist for Philadelphia (3-7-4), and Noah Cates scored. Vladar made 11 saves.
The Blue Jackets took the lead on three goals in a 2:46 span midway through the first period.
Fantilli made it 1-0 Columbus at 10:58 with the teams skating 4-on-4, when he got to the net to finish a give-and-go with Johnson, lifting a wrist shot between the arm and ribs of Vladar.
Johnson made it 2-0 at 12:54 when he redirected Zach Werenski's one-timer from the point past Vladar.
Mateychuk pushed the lead to 3-0 at 13:44 when he scored with a snap shot along the ice from the top of the face-off circles and through traffic.
Cates cut the Flyers' deficit to 3-1 at 9:59 of the second period. Porter Martone's shot from the top of the circles squeezed through Talbot, and Cates beat his man to the net to push the puck over the goal line.
Zegras made it 3-2 at 15:04 of the third period when he banked the puck in off the right hip of Talbot to make it a one-goal game.
