On the brink of elimination, and with the Flyers enduring the latest in a string of goalie shuffles, Boucher stopped 24 shots in yet another relief effort and Leino capped Philadelphia's two-goal comeback by scoring 4:43 into overtime in a 5-4 win on Sunday to force Game 7 in the first-round playoff series.
The deciding game is at Philadelphia on Tuesday to close what's been a tightly contested and topsy-turvy series, in which five of the six games have been won by one goal.
"I've been through some pretty wild and crazy games through my career," said Danny Briere, the former Sabres co-captain who scored twice against his former team. "And today was one of them, the roller-coaster ride that it was. My heart definitely skipped a few beats today."
He wasn't the only one.
Michael Leighton became the third Flyers goalie to start a game this series, before proceeding to become the third Flyers goalie to be yanked after allowing three goals on the first seven shots.
Enter Boucher, who made up for his dreadful performance in a 4-3 overtime loss on Friday, in which he allowed three goals on 11 shots.
And unlike what happened in Game 5, in which the Flyers rallied from a 3-0 deficit before faltering, Leino sealed this victory during a scramble in front.
Kris Versteeg helped set it up. After getting his first shot blocked, Versteeg gained the rebound and flipped the puck at the Sabres net, bouncing it off several players. The puck fell in the crease where Leino -- a step ahead of defender Chris Butler -- slid it into the open side behind diving goalie Ryan Miller.
Scott Hartnell had a goal and assist and James van Riemsdyk also scored for the Flyers, who rebounded after two losses.
Now it's the Sabres turn to bounce back in a season in which they've been counted out before. After a dreadful start to the year and after losing top-line center Derek Roy to a leg injury in December, Buffalo responded by going 29-11-6 in its final 46 games to clinch a playoff spot in its second-to-last game of the season.
PREDATORS 4, DUCKS 2
In Nashville, Tenn., Nick Spaling scored his second goal of the game at 4:53 of the third period and Nashville closed out its first postseason series victory to advance to the Western Conference semifinals.
Steve Sullivan scored a goal, David Legwand had an empty-netter and Jordin Tootoo assisted On Spaling's goals. The Predators won the series 4-2 in their sixth postseason in seven seasons.
Jason Blake scored a power-play goal, and Teemu Selanne also had a goal for the Ducks. Anaheim looked tired early after blowing a lead late before losing Game 5 in overtime. Coach Randy Carlyle went heavily with his top two lines trying to rally.
Anaheim lost in the opening round for the third time in seven playoffs.
BLACKHAWKS 4, CANUCKS 3 (OT)
In Chicago, Ben Smith scored on a rebound at 15:30 of overtime and the defending Stanley Cup champion Chicago a win over Vancouver to force a seventh game in the first-round series.
The Canucks, with the NHL's best record during the regular season, have lost three straight after it appeared they were in control of the series. Game 7 is Tuesday night in Vancouver.
Smith, a rookie, followed in a long, hard shot from the point by teammate Niklas Hjalmarsson that bounced off goalie Roberto Luongo.
Luongo didn't start the game but was called upon in the third period when Cory Schneider had to be helped off the ice when he was injured as he tried to stop Michael Frolik's penalty shot that tied it at 3.