Vinny Lecavalier scored the only goal in the shootout.
Mason said he didn't mind facing a season-high 44 shots.
"I actually enjoyed it. It was nice to get into a game and feel like you're doing something out there," he said after the Flyers' third straight victory. "I was very confident out there. I'm happy with my game."
With Mason pulled for an extra attacker, Schenn ended a 16-game drought without a goal, taking a tipped pass from Scott Hartnell and tapping in his eighth goal to tie the score.
"It feels good. Long overdue. The monkey's off the back," said Schenn, who added: "When you're not scoring, you tend to think a little more out there than normal, and hopefully I can keep it rolling."
Daniel Sedin had given Vancouver a 3-2 lead when his shot went off Mason and then bounced off defenseman Luke Schenn - Brayden's older brother - and into the net with 2 minutes, 48 seconds remaining in regulation.
"Luke's just trying to get back to the net there and it was an unfortunate bounce," Mason said. ". . . I thought right after that goal, that was probably the hardest we were working the entire game."
Luke Schenn, who was minus-3 for the night, was extra appreciative of his brother's tally.
"He said, 'Thanks for bailing me out,' " Brayden Schenn said with a laugh. "He said, 'I got one and you got one.' "
Despite the win, coach Craig Berube was unhappy with his team's performance. The Flyers were badly outplayed and were outshot, 44-27. But they won a shootout in back-to-back games for the second time in franchise history - the other time was in 2006.
Lecavalier made a series of pretty moves and went forehand-backhand-forehand to beat goalie Eddie Lack in the shootout.
"I never played against him, so I wasn't quite sure [how to beat him]," Lecavalier said. "I was trying to figure it out as I was going down the ice. I went back to what worked against Nashville. He's a big guy, and I wasn't sure if he was going be deep in his net or out, but he kind of came out for me to be able to deke him."
Claude Giroux took a career-best nine-game points streak (six goals, 11 assists) into Tuesday. . . . Ray Emery made just his third start in the last 13 games.
Flyers Notes: A Real Shot in Shootouts
Thanks to goalie Steve Mason, the Flyers have improved in shootouts this season. Here are Mason's shootout numbers, compared with Ilya Bryzgalov's in his two years with the Flyers.
Rec. Shots GA Save %
Steve Mason (2013-14) 3-3 20 6 .700
Ilya Bryzgalov (2011-13) 4-7 34 18 .471
The Flyers' statistics this season:
Shots Goals Shooting %
Claude Giroux. . . 6 3 .500
Vinny Lecavalier. . . 4 2 .500
Michael Raffl. . . 1 1 1.000
Brayden Schenn. . . 1 0 .000
Kimmo Timonen. . . 1 0 .000
Sean Couturier. . . 2 0 .000
Matt Read. . . 3 0 .000
Totals. . . 18 6 .333
- Sam Carchidi