Predators captain Shea Weber had a goal and an assist. His 16th goal of the season, 3:33 into the second period, broke a 1-1 tie and helped Nashville to its second win in as many nights.
"It's a good start to the road trip so far," Weber said. "We've got a challenge in Chicago coming up. They're a very good team and we've got to make sure we keep pushing forward and trying to get on a roll here."
The Predators began a road trip Monday with a 4-3 overtime win against the Ottawa Senators. Nashville (28-28-10) plays at the Chicago Blackhawks on Friday.
"Everybody thinks about the slap shot, but probably the wrist shot, to me, is his most effective shot," Predators coach Barry Trotz said. "When he comes in there and he gets to the top of the circle and he snaps it off, it's moving. It's his most effective and he can place it better."
Sabres forward Drew Stafford opened the scoring 2:09 into the game with a power-play goal. Stafford put a rebound of Cody Hodgson's shot past Predators goalie Carter Hutton for his 12th of the season.
Stafford was playing in his 500th NHL game, all with Buffalo, and has 14 points in the past 15 games.
"Drew's really trying to take the leadership role we lost on this team," Sabres coach Ted Nolan said. "We've lost some veteran players, so he's embraced stepping up."
After the Predators gave up a goal on the Sabres' first power play, they stopped them on the next three, two in the second period.
"They've got some pretty skilled players there," Hutton said. "I'm just trying to be aggressive on my part, and the defense helped me out on second chances. I think that was big. From there, I think keeping the two-goal lead was pretty huge for us."
The Predators tied the game with 2:50 left in the first period when Nick Spaling scored a power-play goal. A shot from Weber glanced off Spaling's skate past Enroth for his 13th of the season. Video replay confirmed the puck deflected into the net in legal fashion.
Craig Smith gave the Predators a 3-1 lead at 7:51 of the second period. Wilson set up the goal when he found Smith alone in the slot to fire a slap shot through Enroth's five-hole. It was Smith's 20th goal of the season.
"It's great, a good feeling," Smith said of reaching 20 goals. "We just have to keep moving forward, trying to make a little push here."
Predators center Paul Gaustad, playing his first game in Buffalo since being traded by the Sabres on Feb. 27, 2012, scored an empty-net goal with 1:31 remaining.
"It feels better to get the win," Gaustad said. "It's always nice to be back. The fans here are awesome and they've got a lot of good people here too. I had a lot of good memories, but I couldn't think about it much. We had to get these two points."
Hutton made 23 saves; Enroth stopped 21 shots.
"[Hutton] was really good, he stabilized us when they had a little push," Trotz said. "I think today was his 15th win. That's pretty good for a guy that came in [to the season] with one NHL game."
Nashville last played at Buffalo on March 20, 2011, winning 4-3 in overtime.
This loss was the third in a row for the Sabres (19-38-8). They play 12 of their final 17 games on the road.
"It's a time for us to really come together as a team," Stafford said. "We're going to be spending a lot of time together in close quarters. It's going to be up to us to drag ourselves out of this."
Buffalo's next two games are on the road, against the Carolina Hurricanes on Thursday and New York Islanders on Saturday.
"Their confidence is a little bit rattled right now," Nolan said. "But through tough times like these, you find out true character of certain players, and through the ashes sometimes some people rise."