The victory ran the Kings' (36-22-6) winning streak to six games.
Winnipeg and Phoenix were tied at 67 points heading into the game, one point behind Dallas for the final wild-card spot in the Western Conference. Vancouver was one back of the Jets and Coyotes.
Vancouver was visiting Dallas on Thursday night and Phoenix was hosting Montreal.
Los Angeles outshot the Jets 11-7 in the opening frame.
Winnipeg didn't get its first shot of the second period until almost seven minutes in, but the Jets scored on their 11th of the game.
But the jubilation of the MTS Centre only lasted 42 seconds.
Brown scored his 12th goal of the season after centre Jarret Stoll sent a long backhand pass across the front of the net and Brown got his stick on it. The puck trickled across the goal-line past Pavelec at 12:45.
The Kings went up 2-1 on a Winnipeg giveaway.
Jets defenceman Tobias Enstrom was at the boards by the Kings' bench and made a pass across the ice that was supposed to be for Jokinen, but Richards intercepted it halfway, crossed the blue-line and then fired a shot by Pavelec at 16:15.
Los Angeles also outshot the Jets 10-6 in the second. The Kings are now 19-0-0 this season when leading after the second period.
With Jets forward Blake Wheeler in the penalty box for high-sticking, defenceman Martinez scored unassisted at 15:51 with a shot on Pavelec's blocker side.
Both teams were featuring some new lines, but for different reasons.
The Jets had to juggle all four lines from Tuesday's 3-2 overtime loss to the New York Islanders because of injuries.
Winnipeg rookie centre Mark Scheifele sprained the medial collateral ligament in his right knee during the loss. The second-line centre is out for at least four weeks and possibly the rest of the regular season.
Forward Chris Thorburn was also injured in the game and is listed day-to-day with an upper-body injury.
Jokinen was centring the second line with Kane and Byfuglien. Michael Frolik, who's only played a few games at centre during his six-year NHL career, was put in the middle with Matt Halischuk and Devin Setoguchi.