The Wild (10-8-3) had lost two straight games.
"We all know we can play better," Granlund said. "At the same time, we got the win and that's all we need right now. These kinds of games happen and we've just got to move on and get ready for the next one."
Jordan Nolan scored his first two goals of the season for the Sabres (5-13-4), who have lost seven straight (0-5-2).
"It's a game of mistakes, and it's decisions and choices at the wrong time of the game," Sabres coach Phil Housley said. "We get the first goal [and] all we have to do is continue to stay the course. It's one mistake here, one mistake there that guys are making the wrong choices and not playing the right way."
After Nolan's first goal with Buffalo cut the Minnesota lead to 3-2 at 2:01 of the second, Niederreiter's second goal made it 4-2 at 7:57.
Granlund's second of the game made it 5-2 on the power play at 15:56 of the second when he tipped a shot by Koivu through Lehner's legs.