Jost gave the Sabres a 1-0 lead at 2:59 of the first period, deflecting Rasmus Dahlin's shot from the point.
Lundell tied it 1-1 at 5:02 with a backhand shot through traffic with his back toward the goal.
Stenlund gave Florida a 2-1 lead at 8:11 with a short-handed goal. He intercepted a pass and drove down the ice, beating Luukkonen with a backhand-to-forehand shot.
Quinn tied it 2-2 at 9:48 on the power play, scoring on a rebound of Bowen Byram's shot.
Alex Tuch took a high-sticking penalty at 19:25 of the third period, but the Panthers were unable to score on the power play, which included a 4-on-3 advantage for 1:25 of overtime.
Buffalo was 3-for-3 on the penalty kill, which included a five-minute major penalty.
"Those were huge kills and it would have been nice to win after those,'' Sabres defenseman Owen Power said. "It is what it is. Obviously, we didn't come out with it.''
The Panthers have one more game remaining in the regular season, hosting the Toronto Maple Leafs on Tuesday.
"If it makes more sense to rest (players), we'll do it ... If we get the chance to compete for something, we're going to compete for it,'' Florida coach Paul Maurice said.
NOTES: Reinhart's 55 goals are the third most in a single season in Panthers history. Pavel Bure scored 59 in 2000-01 and 58 in 1999-00. Reinhart's 10 game-winning goals are the second highest single-season total in team history behind Bure (14 in 1999-00). … Bobrovsky is 396-224-55 with the Panthers, Philadelphia Flyers and Columbus Blue Jackets.