Minnesota won its sixth straight and dealt the Kings their third consecutive loss.
Hackett, 21, played in an NHL game for the first time Tuesday when he came on to replace the injured Josh Harding in a 2-1 victory over San Jose. He had a 2.11 goals-against average with Houston of the American Hockey League this season.
His teammates helped things along by giving him a 3-0 lead through two periods. Mikko Koivu scored 24 seconds into the game on a wraparound shot and Darroll Powe and Marco Scandella added second-period goals.
Dustin Penner ended Hackett's bid to turn in a shutout in his first start, scoring on a wrist shot 3:59 into the third. Cody Almond restored Minnesota's three-goal lead with 8:18 to play.
Jonathan Quick gave up four goals on 25 shots.