After Nashville built a 3-1 lead, backup goaltender Carter Hutton helped stave off a Buffalo attack that controlled possession and outshot Nashville 11-5 in the second period.
"Keeping that two-goal lead going into the third was pretty huge for us, confidence heading out there," Hutton said. "After last night, we knew we were going to lock it down and play our game."
Hutton had allowed multiple goals in eight consecutive starts entering the game, but was stout on Tuesday.
"Hutton was really good," Trotz said. "He stabilized us when they had a little push."
The Predators arrived in Buffalo after 2 a.m. after Monday's game at Ottawa and skipped their morning skate before having to fight off a slow start to Tuesday's game.
"It was penalties right off the bat," Trotz said. "First five minutes, we were killing the four. That's a hard way to get going, especially when you're in back-to-back. Those are hard minutes."
An early power play helped Buffalo take a 1-0 lead at 2:09 of the first as Stafford pulled a rebound away from Hutton's left pad to score his 12th goal of the season.
The goal ended a 0-for-11 slump for the Sabres power play, and came in Stafford's 500th career NHL game.
Yet aside from Stafford's line, Buffalo had trouble generating offense.
"There was only one line basically going," Sabres interim head coach Ted Nolan said. "You're not going to win too many games doing that."
Nashville's equalizer came at the 17:10 mark of the first period, as Spaling used his skate to deflect a Weber shot past Jhonas Enroth. The power-play goal came on Nashville's only attempt with the man advantage.
Tied at 1 after 20 minutes, Weber picked up a drop pass from Wilson and beat Enroth to make it 2-1 at the 3:33 mark of the second.
Smith doubled Nashville's advantage at 7:51. His low slap shot from just in front of the blue line beat Enroth between the legs.
The goal was Smith's 20th of the season, a career best.
"It's great, a good feeling," Smith said. "We just have to keep moving forward, trying to make a little push here."
The game was a shaky one for Enroth, who had played well since Buffalo traded Ryan Miller to St. Louis on Feb. 28.
Buffalo's Zenon Konopka was challenged to fight by Gaustad at 9:20 of the second after the Sabres forward put an open-ice hit on Viktor Stalberg. Gaustad received a two-minute instigator and 10-minute misconduct in addition to his fighting major.
Trotz thought the penalty was questionable, and appreciated Gaustad's response.
"To me that was a really good glue play," Trotz said. "We thought it was a questionable hit and that's what you want your team to stand up for each other.
"Gaustad knows how tough Konopka is, and that's why he's so valuable to us. He brings those intangibles. He does what's right and is very detailed in his game."
Hutton made a big save on Tyler Ennis moments later. Stafford worked the puck behind the net before passing to Cody Hodgson, whose high shot was gloved by the Nashville goaltender.
"He made a bunch of great saves that kept us in it," Wilson said of Hutton. "It could have been a bit of a different game if they got a couple at the beginning there."
The Sabres finished 1 for 4 on the power play.
Gaustad added an empty-net goal at the 18:29 mark of the third period to a chorus of boos from a crowd that chanted his nickname "Goose" when he was a Sabre.
"We joked about that," Gaustad said. "I didn't know when I was here if they were booing me or saying my name. Some of the best fans and people on Earth. Salt of the earth people."
Nashville finishes a three-game road trip on Friday in Chicago, while Buffalo begins a stretch of playing 12 of its next 17 on the road.
"Their confidence is a little bit rattled right now," Nolan said. "But through tough times like this you find out true character of certain players and through some ashes sometimes there rises some people."
Sabres LW Matt Ellis played in his 300th NHL game. ... Patrick Eaves was scratched after going pointless in his first three games with the Predators after being acquired in a trade with Detroit for David Legwand. ... Sabres rookie C Zemgus Girgensons missed his third game with an undisclosed injury.
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BUFFALO, NY - MARCH 11: Drew Stafford #21 of the Buffalo Sabres scores Baffalo's first goal against Roman Josi #59...