Mrazek said he was nervous all day waiting for the game to start.
"I was really excited for tonight's game," he said. "The day was so long for me, felt like we were playing at midnight, not 7. I was waiting for it. Happy it's over and we got the two points."
Artemi Panarin scored, and Sergei Bobrovsky made 18 saves for the Blue Jackets, who are 1-3-1 in their past five games.
Columbus (30-26-5, 67 points) is tied with the New York Islanders for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
"I'm not going to pick apart the team because we didn't get 50 shots tonight," Blue Jackets coach John Tortorella said. "This is the way the games are, they're going to get tighter and tighter. First period, we don't get any momentum, we take two penalties. And I did think we struggled just making simple plays. But I think our guys gathered themselves and played two good periods."
Patrick's power-play goal at 9:49 of the third period put the Flyers ahead 2-1. Giroux drew a tripping penalty against Blue Jackets forward Brandon Dubinsky and then won the ensuing face-off against Cam Atkinson on the left side of the Columbus zone. Giroux got the puck from Sean Couturier and set up Gostisbehere for a one-timer that Bobrovsky stopped, but Patrick poked in the rebound to extend his goal streak to three games.
"The last 15-20 games I've been feeling myself, feeling confident, trying to contribute as much as I can on both sides of the puck," said Patrick, who has scored a goal in three straight games, five in his past 12.
Panarin gave the Blue Jackets a 1-0 lead at 12:51 of the second period when he kept the puck on a 2-on-1 rush and beat Mrazek. It was Panarin's 200th NHL point.