Ryan Johansen had a goal and an assist, and Juuse Saros made 28 saves for the Predators (19-17-6), who have lost three straight.
"I think we felt good going into the third, obviously had a lot of momentum," Predators captain Roman Josi said. "Gave up one on the power play, the short-handed goal, which was the tiebreaker.
"That can't happen on the power play, when you have a chance to score. If you can't score, [at least] get some momentum. Can't get scored on."
Okposo gave the Sabres a 4-3 lead at 6:43 of the third, redirecting Ilya Lyubushkin's shot through his own legs and past Saros. Okposo won a puck battle against Josi and Tommy Novak to set up the goal.
"[Okposo] is a worker," Sabres coach Don Granato said. "He's a leader by virtue. That was vintage Kyle Okposo. The work, the combination, you see that grind, you see that work and then to finish, you see a fine touch, a fine skill. That's [Okposo]."
Quinn scored at 16:49 for the 5-3 final.
"It was nice to see it go in that time of the game, especially after missing that open net a couple of minutes earlier," Quinn said.