Jake Muzzin scored, and Jack Campbell made 21 saves for the Kings (5-9-1), who had won two in a row.
Parise put Minnesota ahead 2-1 at 14:42 of the second period with his 339th NHL goal, most among active American-born players.
Parise is the fifth player born in Minnesota to reach the milestone, joining Phil Housley (1,232), Neal Broten (923), Dave Christian (773) and Matt Cullen (714).
The Kings went on a power play with 1:54 remaining in the third period when Marcus Foligno caught Dion Phaneuf with a high stick. Campbell came off for an extra attacker with 1:15 remaining, but Granlund scored shorthanded at 19:57 to make it 3-1.
"I thought we were pretty smart with our puck management with the dangerous players that they have," Parise said. "But we did a good job holding on, getting the puck out of our zone and not turning it over."
The Wild tied it at 1-1 when Niederreiter scored on the power play at 14:23 of the first period. It was the first goal for Niederreiter, ending a 22-game drought in the regular season dating back to March 24, 2018.
Parise found Niederreiter in the paint for a tap-in. Niederreiter was visibly relieved, letting out a yell as he was surrounded by his teammates, and Wild coach Bruce Boudreau said the forward's play improved immediately after scoring.
"Right after that he looked a lot faster for the rest of the game," Boudreau said. "It's obviously weighing on your mind when you're a scorer and you haven't scored in a long time."
Muzzin put the Kings in front 1-0 at 4:42 with his first goal of the season, a wrist shot from the left circle.
Alec Martinez had the assist, giving him three in the past two games.
The Kings had 14 shots in the first period and a total of 14 over the final two periods.
"I don't think we played enough, obviously, in their zone," Kings center Anze Kopitar said. "Maybe they came out a little slower in the first period and then played better as the game progressed. I thought we played a decent game but we need to capitalize on the chances."
