Elvis Merzlikins made eight saves on 12 shots before being removed 3:40 into the third period. Matiss Kivlenieks made two saves.
Columbus, the New York Islanders and Carolina Hurricanes are one point behind Philadelphia in the Metropolitan and tied for the first wild card into the Stanley Cup Playoffs from the Eastern Conference.
The Blue Jackets outshot the Flyers 29-15, but coach John Tortorella said the quantity did not reflect the quality.
"We need to funnel pucks (to the net)," he said. "We made too many extra plays. ... I don't think we played a bad game, certainly not a 5-1 game, but we need to continue to remind ourselves how we have to play the game."
Blue Jackets captain Nick Foligno said, "Disappointing when you look up at the shots on net, and I think we outshot them a lot tonight and had some moments when we outplayed them. But we have to find answers to score goals and keep them out of our net."
The Flyers said their game plan was to start by playing fast and sustain that tempo. They scored twice in the first 4:30.
Hayes' shot from the left side along the goal line banked in off Merzlikins' back to make it 1-0 at 3:28, and Sean Couturier scored through Merzlikins' five-hole on a breakaway 1:02 later made it 2-0.