Marian Gaborik broke a 2-2 tie, 2:01 into the third to open the floodgates. With Josh Morrissey off serving a hooking penalty, Gaborik took a pass and curled off the near wall, walked in and fired a shot far side, under the glove, to give the Kings their first lead of the night.
Another PPG - the Kings' third of the night - sealed the win just 1:56 later, as Drew Doughty hammered a one-timer from the top of the zone clean past Hellebuyck to give the home side a two-goal cushion.
Tanner Pearson scored shorthanded to round out the offence at 9:21.
Connor Hellebuyck made 31 saves.
With the loss, the Jets' winning streak is halted at three.
"We've talked about (discipline) all year," Perreault said. "Obviously our PK has struggled and if you're in the box a lot, it's definitely not helping the team. We've got to stay out of the box if we want to have any chance of winning games."
The Jets were the better team in the opening 20, scoring twice and taking a 2-1 lead into the first intermission, but the Kings - who were fighting for their playoff lives - took over the game with a dominant middle frame.
Finally, after more than 15 minutes buzzing around the Winnipeg net, they hit pay dirt.
With Jeff Carter supplying the screen in front, Jake Muzzin filtered one through from the left point, beating Hellebuyck clean on the glove side as he battled to find the puck through traffic.
The goal came at 16:05, tying the game at two after the Kings doubled up the Jets on the shot clock (16-8). Hellebuyck was excellent, keeping his team in the game with a number of big saves late to preserve the tie after 40 minutes of play.
"It's 2-2 going into the third and you've battled fairly hard on the road, but we got into the box and that was the end of it," said Head Coach Paul Maurice.
"We've got to find someone to get in front of a shooting lane."