Mike Fisher, Ryan Johansen, Filip Forsberg and Ryan Hartman scored for Nashville (48-14-10), which has clinched a Stanley Cup Playoff berth and leads the Winnipeg Jets by 10 points for first place in the Central Division.
The Predators have won four games in a row and are 14-0-1 in the past 15, passing their 14-game point streak (9-0-5) from Feb. 12-March 9, 2016.
"I think we were fortunate in the second period," Nashville coach Peter Laviolette said. "The scoreboard went our way, but everything else went Buffalo's way in the second period. So, we're fortunate, we take it, and we move on and try to get better, which I thought we did."
Rinne is the seventh goalie in NHL history to win 40 games in a season three times.
"He's just so motivated, he's such a professional, and he's so motivated on this team and he's the reason we're where we're at in the standings," Johansen said. "He's been phenomenal for us all year; he's a man on a mission right now and he's really enjoying it and having fun. Every day, he's the leader in our room and he leads by example, and no one competes as hard as him on a daily basis. It's great to be his teammate and watch him play and have success this year."
Linus Ullmark made 28 saves in his second start of the season for the Sabres (23-37-12), who have lost three of four games (1-2-1) and were eliminated from playoff contention Saturday.
"Really happy with the way we played against the best team in the League at this point," Sabres coach Phil Housley said. "Exactly the way we want to play. I thought we were fast. We were aggressive. ... We didn't seize our opportunities, but I can't fault the way our guys played."
Fisher gave the Predators a 1-0 lead at 12:29 of the second period when he tipped a shot by Miikka Salomaki that had deflected off linemate Scott Hartnell. It was his second goal since coming out of retirement March 2.
