Asplund tapped the puck into an open net after receiving a pass from Victor Olofsson, who got around Trevor Zegras before warding off Jamie Drysdale to make the play.
"I think that's been one of the things we've been doing really well throughout the year here," Asplund said. "Even if we're down one or we're up by three like today … we still try to manage the calm we have in the group and stick to our game and do what we do to make us successful. I think we've been doing that all year and even today. So that's a good thing from the group, I think."
Zemgus Girgensons and Arttu Ruotsalainen also scored for the Sabres (5-1-1), who were playing the first of a four-game road trip. Craig Anderson made 34 saves.
Simon Benoit scored his first NHL goal, and Anthony Stolarz made 25 saves for the Ducks (2-4-2), who are 0-3-2 in their past five games.
"There have been so many encouraging signs with the way we've played in games, and there's been letdowns at certain times that have certainly cost us," Anaheim forward Adam Henrique said. "You look at playoff teams and teams that get in, and the difference is those games. And it is a long season, but come that time, you're four, five points out in crunch time, and you run out of games. … Those are certainly learning points [that separate] a team on the outs from a team getting in come playoff time."
The Ducks outshot the Sabres 17-12 in the first period, including getting 10 in the opening seven minutes, but Girgensons gave Buffalo a 1-0 lead at 15:03 from the left circle after Stolarz gave up a big rebound on Kyle Okposo's initial shot.
"It's big. Any time a goalie can give you big stops, it's a big relief to the team," Girgensons said. "It can really swing the momentum of the game. It can take the air out of them and kind of give us momentum."