Flynn scored a game-tying goal with under 4 minutes to play and Matt Moulson scored the scored the only goal of the shootout to lift Buffalo to a 5-4 victory over the Ottawa Senators on Monday night for the Sabres' sixth straight home win.
"We believe in ourselves and I think they believe in us, too," Flynn said, referring to the home crowd. "It's fun when you're out there playing in front of these fans."
The six-game home streak is the Sabres' longest since January 2007, and the win also gives Buffalo a season-high four-game win streak overall heading into Tuesday's game at Winnipeg.
"This group of guys, they're starting to believe in themselves," Sabres coach Ted Nolan said.
Moulson, Marcus Foligno and Rasmus Ristolainen also scored in regulation for Buffalo, which improved to 10-3 since starting the season 3-13-2.
The surprising Sabres are now four points back of the Eastern Conference's final playoff spot.
"I think it's one of those things where you turn the corner and you just hope you keep taking off," Foligno said. "It's been a while since the feeling has been like this in this room. It's just positive energy."
Alex Chiasson had a goal and an assist for the Senators, and Bobby Ryan, Curtis Lazar and Mark Stone also scored.
"We didn't seem to have the jump that we had the previous games," Senators coach Dave Cameron said. "Our execution, especially the passing, was a bit sloppy."
The game was moved from Feb. 20 to accommodate the rescheduled Nov. 21 game between the Sabres and New York Rangers.
Buffalo's Jhonas Enroth and Ottawa's Robin Lehner both had 29 saves through overtime. Enroth also stopped Mika Zibanejad, Kyle Turris and Ryan in the shootout, while Lehner stopped Tyler Ennis and Zemgus Girgensons.
Buffalo had the first five shots of the game, including an attempt by Cody Hodgson as he glided into the slot and put a wrist shot off the cross bar 2 1/2 minutes into the game.
Enroth made a sliding right pad save to deny Clarke MacArthur after a deflected pass, but Ottawa scored less than a minute later.
Zibanejad won a loose puck to Mike Hoffman, who pushed a spinning backhand pass through the crease to Ryan for the goal.
Sabres defenceman Nikita Zadorov flipped a puck in from the left point that arched into the slot, where Chris Stewart redirected the puck past Lehner with a baseball-type swing of his stick. After video review, it was deemed that Stewart's stick was above the crossbar and the goal was disallowed.
The Sabres tied it up at the 4:11 mark, as Brian Gionta moved off the half wall to find Stewart to the right of the goal. Stewart passed the puck to the left circle, where Ristolainen beat Lehner along the ice to make it 1-1.
Buffalo secured its first lead when Moulson dug Andrej Meszaros' point shot free from Lehner, and backhanded the loose puck into the goal.
"Sometimes you get lucky," Moulson said. "I thought I got a piece of it when Meszaros shot it and it went in. But I was lucky enough to be there, and I'll take those goals."
Just 32 seconds later, Brian Flynn who Foligno on a 3-on-2 to make it 3-1.
Ottawa halved its deficit when Stone finished Turris' pass on a 3-on-2 with 6:28 left in the second.
The Senators needed just over 2 minutes of third-period play to tie the score, as Lazar crashed the crease to jam a loose puck past Enroth for his first NHL goal.
Ottawa took a 4-3 lead when Enroth misplayed Chiasson's low backhand shot.
The Senators managed 10 of the period's first 11 shots, but Flynn shot Foligno's rebound past Lehner to tie the score with 3:29 remaining in regulation.
"Timely scoring, great goaltending and I still think we can play a bit better," Flynn said.
Ottawa carried play in overtime, outshooting Buffalo 4-2, before Moulson found the winner in the shootout.
"No matter what happens we keep battling, stay focused and compete," Moulson said. "And when you do that, you can have a lot of success."
NOTES: Sabres C Torrey Mitchell was injured blocking a shot in the first period. Buffalo called up Mikhail Grigorenko from Rochester after the game. ... The Sabres are 6-0-1 when leading after two periods.