Texier tied the game 1-1 at 15:02 when he scored from the high slot during a delayed penalty.
Bobby Brink, who had been scratched the three previous games, put the Flyers ahead 2-1 at 1:11 of the second period with a power-play goal.
"I knew that I was going to have a lane there," Brink said. "We've kind of talked about shooting and the front of the net guy setting a good screen and 'Beezer' [Farabee] did that. When he sets a screen like that, you've just got to put it in a spot, and it ended up going in."
Poehling made it 3-1 at 6:41 when he finished a 2-on-0 short-handed rush. The goal was upheld after video review showed the puck completely crossed the goal line.
Columbus went 0-for-5 and didn't have a shot on goal on the power play.
“The power play hurts us," Jenner said. "That's on us. We have chances, we can't give up a shorty. We have chances to get back in it too. We have to find a way to get it going. You can see it but it's hurting us."
Jenner's goal made it 3-2 at 17:57. He was at the net when a shot by Ivan Provorov went off his leg and in. It was Provorov's first game in Philadelphia since he was part of a three-team trade that included the Los Angeles Kings on June 6. The defenseman played his first seven NHL seasons with the Flyers.
Travis Konecny scored to make it 4-2 at 12:40 of the third period after the Blue Jackets let the puck go into their zone on a line change. York scored an empty-net goal at 17:34 for the 5-2 final.
NOTES: Blue Jackets defenseman Damon Severson left the game after Poehling's short-handed goal because of an upper-body injury. Coach Pascal Vincent did not have an update after the game. ... Columbus' nine-game skid is its longest since it lost nine in a row (0-7-2) from April 8-25, 2021. ... The Flyers lead the NHL with five short-handed goals. … The Flyers went 1-for-4 on the power play after going 2-for-4 in its 4-3 overtime win against the Vegas Golden Knights on Saturday. The Flyers have scored power-play goals in consecutive games; they also did it Oct. 26-28. ... Philadelphia defenseman Sean Walker extended his point streak four games (one goal, four assists) with an assist on Poehling's short-handed goal. ... Flyers forward Owen Tippett had his four-game goal and point streaks ended.