Berube was on the bench a day after Peter Laviolette was fired after a 0-3 start. Laviolette dealt with rumors of his firing last season, a year in which the Flyers missed the playoffs after the lockout-shortened season.
With Berube calling the shots, the Flyers scored their season high for goals. So, there's still work ahead.
Steve Mason had 33 saves for the Flyers.
Brad Boyes scored for the Panthers.
Mason stopped all 12 shots in the first period and the first 12 of the second until Boyes scored his first of the season with 6 seconds left.
Mason, who improved to 5-0 against Florida, came up big when he stopped Shawn Matthias on a short-handed breakaway early in the second.
The Flyers held on and avoided their first 0-4 start in franchise history.
Berube comes steeped in the orange-and-black tradition, with 20 goals and 54 points over parts of seven seasons with the Flyers. He played for four other teams over a 17-year career and his 3,149 penalty minutes are seventh in NHL history.
Berube, in his seventh season coaching within the organization, was promoted to replace Laviolette. He is the 18th coach in franchise history.
The Flyers' offense came to life in the first period against Tim Thomas. Thomas had been sensational in his career in Philadelphia, going 8-0 with a 1.86 goals-against average and a .947 save percentage.
He left the game with a lower-body injury. He appeared to get tangled with teammate Mike Weaver in front of the net and hit the ice. Thomas bolted straight for the locker room and never returned.
Jacob Markstrom took over.
Thomas was pulled after the second period in Saturday's 7-0 loss to St. Louis. He allowed five goals on 28 shots.
Thomas allowed two quick goals in the first against the Flyers.
Schenn punched in a rebound for his second goal of the season. Thomas was out of position after he appeared to get hurt, allowing Coburn to score his first goal of the season.
The Flyers scored two goals for the first time this season. With team captain Claude Giroux without a point in the first three games, the Flyers were outscored 9-3. Just one goal in each game.
The punchless offense is one reason Laviolette was fired just three seasons after he led them to the Stanley Cup finals. The Flyers know they have to play better.
"It was a tough day yesterday," Giroux said before the game. "I was with Lavy for a while, and to see him leave is a little sad. But it's the business part of it. We need to understand that."
The Flyers got a brief scare in the third when forward Scott Hartnell was slow to get up after defenseman Erik Gudbranson plowed him into the boards. Hartnell needed medical attention on the ice, but skated off on his own power. Gudbranson earned a game misconduct.
Notes: There was a brief scrum in the third that saw Flyers F Jay Rosehill get hit with 4 minutes for roughing and a 10-minute misconduct. ... Chicago Blackhawks VP of hockey operations Al MacIsaac presented Flyers G Ray Emery with his 2013 Stanley Cup champions ring. Emery went 17-1 for the Blackhawks last season. ... "Machete Kills" stars Alexa Vega and Danny Trejo were at the game.