The tally returned the team goal-scoring lead to Granlund after Eric Staal tied him during the third period in Washington on Tuesday.
For Koivu, it was his 22nd career short-handed point, which moved him ahead of Wes Walz for the most by a Wild player in franchise history.
2. With the game tied at 1 late in the third period, Carolina's Victor Rask scored the winning goal.
It was the 16th goal of the season for Rask, who wheeled out of the right corner and powered to the front of the net, slipping the puck through the five-hole of Wild goaltender Devan Dubnyk.
Until that point, Minnesota (43-20-6) had done a serviceable job limiting scoring chances, but the Wild surrendered too much ice to Rask, who was able to work his way to the top of the crease before finding resistance.
"They never quit right down to the last second," said Wild coach Bruce Boudreau. "The guys are feeling it. It's been a long trip. We had opportunities. We just didn't score."
The goal capped a tough road trip for Minnesota, which finished its five-game swing with just one victory. The Wild returns home to play four of its next five games on Xcel Energy Center ice beginning Saturday against the New York Rangers.
"We gotta bring it ourselves. It's nice to be in front of the home crowd, but we gotta bring it ourselves," said Wild forward Charlie Coyle. "It starts with us inside here. That's what we gotta do. We gotta bring our compete level, stick to our structure and turn this thing around. It's one game at a time."