Lawson Crouse had two goals and an assist, and Kevin Stenlund had two assists for the Mammoth (37-28-6), who were coming off a 4-1 loss to the Anaheim Ducks on Friday but have won three of their past four games. Vejmelka made 33 saves.
Utah holds the first wild card into the Stanley Cup Playoffs from the Western Conference, five points ahead of the Nashville Predators.
“I loved the urgency and I loved the intensity of our game,” Tourigny said. “That’s a heavy team on the other side. It was important for us to be [competitive] in our battles."
Quinton Byfield had a goal and an assist, and Alex Laferriere also scored for the Kings (28-25-17), who have lost three in a row (0-1-2), including 4-1 to the Buffalo Sabres on Saturday. Kuemper made 30 saves.
Los Angeles is two points behind Nashville for the second wild card.
“I thought it was a real gutsy effort by us. It's probably our best second period of the year,” Kings interim coach D.J. Smith said. “We've had games where it's gone the other way for us and then we get a bit of a bounce and tie it. ... It's unfortunate to lose that point, but we pick up a big point as well and we're still in the fight.”
Crouse opened the scoring at 7:04 of the first period. He gave the Mammoth a 1-0 lead by beating Kuemper from in tight with a one-timer off a pass from John Marino, who stole the puck from Samuel Helenius along the goal line.
“It's easy when you get rewarded when you go to the net, but you have to do it consistently,” Crouse said. “Just because you go one time and you score, it doesn't mean it's going to continue to happen. You've got to just build on repetitions and repetitions and going there, and then eventually good things start to happen. It was a nice night for that.”