Mark Pysyk scored the tying goal with 7:57 remaining, Ukko-Pekka Luukkonen was lights out down the stretch and Tage Thompson scored the decisive goal in a shootout to clinch a 3-2 win for Buffalo.
The Sabres have won two games in a row to open their road trip, which concludes Friday against the Penguins. What was a seven-game winless skid has flipped into a three-game point streak dating back to Saturday's shootout loss to the Capitals.
Granato, as he has all season, hammered a message of playing with confidence and keeping the focus on improvement after a series of high-scoring losses to Seattle, Carolina, and Florida early in the month. He was disappointed when those games bled into a tentative 2-0 loss to Anaheim.
Things turned from there, even if the results were slow to follow. The Sabres had the game-tying goal incorrectly taken off the board in a 2-1 loss to the New York Rangers, one of the premier teams in the Eastern Conference. They rang two posts in the shootout against the Capitals.
"We've had what you might think is bad luck if you recount games," Granato said. "But you've got to keep moving on. And I say moving on - never, ever, ever stop growing and focus on that growth.
"I refer to our practices a lot and you watch our practices. They're intense. The guys are practicing with intent to get better. You see them improve in practice execution and you know there will be a lag, but eventually they're going to start executing at that proficiency in the game."
The Sabres played undeterred hockey in the face of physical play from the Wild and a solid first period from goaltender Cam Talbot. They outshot the Wild 21-16 during the opening 20 minutes but trailed 1-0 on a goal from defenseman Jon Merrill.
Dylan Cozens (more on him in a moment) scored the tying goal in the second period before Kaprisov, the reigning Calder Trophy winner, found the five-hole during the final minute.
"I think [we stayed] calm throughout that," Thompson said. "Obviously, we had a really good first period and they had the lead, but it didn't affect us. We just kept going and we got the result."
In doing so, they checked a box that was previously unfilled this season. Just as the Wild had not lost when leading, the Sabres had not yet won a game in which they trailed after two periods entering Thursday.
Again, this is a team that's growing.
"That's our entire focus is on growth," Granato said. "We're gonna stay with it regardless of results."