"I told the team afterward to just keep believing," Berube said. "It's tough, but we're going in the right direction. I thought our guys competed really hard and did a lot of good things out there."
Defensemen Braydon Coburn and Nick Grossmann appeared to be out of position when Kesler pounced on the loose puck to score the game-winner.
The Flyers wasted two goals from Tye McGinn. They are 1-3 since Berube replaced Peter Laviolette.
The Flyers, who host Pittsburgh on Thursday, carried a 2-1 lead into the third period before Vancouver rallied. They have been outscored, 10-2, in the third period this season.
"Confidence is the biggest thing," Berube said. "You've got to go out and take it to the other team in the third periods and win the game. We're kind of sitting back a little bit and waiting for something bad to happen. We've got to get over that hump."
"It's haunted us for the last two seasons," winger Jake Voracek said of the team's third-period doldrums. "We have to find a way to win those games. . . . It's like we're scared to make something happen on the ice."
Higgins, left alone in front, tied it at 2-2 with 12 minutes, 29 seconds left in the third period, one-timing a Henrik Sedin pass from behind the net. It was Sedin's 800th career point.
Mason again was solid. Vancouver's first goal was scored when Jannik Hansen dumped the puck into the Flyers zone and it caromed crazily off the boards while Mason was caught behind the net. Kesler tapped the rebound into an empty net, tying the score at 1-1 with 7:24 left in the first period.
The goal was scored 10 seconds after McGinn backhanded a rebound past Roberto Luongo.
Early in the second period, after Voracek's crossing pass was deflected by Claude Giroux, McGinn scored after digging out the puck out front, putting the Flyers ahead, 2-1. Later, two defensive breakdowns erased McGinn's heroics.
"It's frustrating, but we're getting better every game and that's how we have to look at it," Giroux said. "That's a fact. If anybody knows anything about hockey, they know we played a good game. We played our best game [of the season]."
The Flyers offense continues to struggle. They managed just 22 shots and have scored a total of 10 goals - their lowest seven-game total at the start of the season in franchise history. Their power play was 0 for 2 and has not connected in its last 17 tries.
The Flyers under Peter Laviolette:
W L GF GA
0 3 3 9
The Flyers under Craig Berube:
W L GF GA
1 3 7 11