Sean Couturier and Jamie Drysdale each scored, and Dan Vladar made 16 saves for Philadelphia (34-24-12), which had its three-game winning streak and six-game point streak (5-0-1) ended.
The Flyers are five points out of the second wild-card spot with 80 points.
"I think we didn't execute for about five minutes in there in the second (period) and it cost us the game," Couturier said. "Other than that, I thought we played a good game."
Columbus took over early in the second period, scoring twice in a 1:44 span with Werenski leading the charge.
"He's one of the best in the game right now," Marchment said. "He does so many good things every night for us. It's pretty cool to watch."
On the first shift of the period, Werenski skated through the middle of the Philadelphia zone, drew two defenders toward him and found Olivier open in the right face-off circle for a goal that tied the game 1-1, 44 seconds in.
"Realized it was a 3-on-2, tried to get to the middle of the ice and drive both 'D' to me, and I had two options on both sides of me," Werenski said. "The easier play was to my forehand, so it's a great play by 'Ollie' to finish it."
He then put the Blue Jackets ahead 2-1 at 2:28 when he beat Vladar under his glove with a wrist shot from the hash marks.
After what Bowness called "probably one of the worst" first periods the team has played since he was hired as coach Jan. 12, he said it's no surprise that it was Werenski stepping up.
"He's able to do that when things aren't going good, take control," Bowness said. "The whole team struggled in that first period, let's not kid ourselves. So then when that happens, you need your better players to take over and set the tone. You look at that huge goal 'Ollie' got us right off the bat, set up by 'Z.' You need your better players to set the tone and they did that."