"It just shows that we care. We want to win and we're not quitting," Byfuglien said.
But the veteran defenseman wasn't viewing the victory as an example that the Jets, who are last in the Central Division, can measure up to the Pacific Division-leading Kings, who dropped their third game in a row.
"We can measure some things, but for the most part we didn't overly beat them," said Byfuglien, who scored his 17th goal of the season.
"It was just a couple nice bounces our way and we got (the puck) in. For the most part, they controlled the game."
Both Byfuglien, 15 seconds into the third period, and Postma, at 2:54, fired shots from the point that flew past a screened Jonathan Quick, who made 20 saves.
Ondrej Pavelec had 33 stops for the Jets, who ended a four-game homestand (2-1-1).
Anze Kopitar scored his 25th goal of the season on the power play at 9:25 of the second period for the Kings.
Kings defenseman Drew Doughty said his team, which tied their longest skid of the season, has to get back on track.
"You can't be losing three games in a row at any time throughout the season," said Doughty, whose assist gave him 48 points.
"It's really frustrating that we did this, and we need to fix things, like I said. And we need to get winning hockey games, because right now we're blowing our spot at the top of the division and near the top of the conference."
The Kings outshot Winnipeg 14-4 in a scoreless first period and increased the gap to 29-14 after two periods.
"It's all about building for next year at this point for us," Stafford said. "It's habits. We could have easily folded up tonight against a team like that was really bringing it to us.
"We followed (Pavelec's) lead. The way he was playing kept us in the game."
Jeff Carter, who also assisted on Kopitar's goal, said his team struggled.
"You can't give up three or four goals a game if you're not scoring," he said. "So, we've got a lot of work to do. It starts from the top and trickles down and we've got to get going."
Nikolaj Ehlers was back on Winnipeg's top line with Scheifele and Wheeler wearing a full cage. The rookie left wing missed the past 10 games with an eye injury from when he took a puck to the face during a March 3 game against the New York Islanders.
Winnipeg veteran defenseman Mark Stuart was also back on the ice after missing 18 games because of a broken hand.
The Jets head out for a two-game road trip, starting Saturday in Buffalo. Los Angeles is home to Edmonton on Saturday. ... Jets defenseman Tyler Myers has been shut down for the season. He had minor knee surgery Thursday that needed to be done before he could undergo hip surgery that needs 16 to 20 weeks of recovery time.