Weaver, playing in just his 32nd game this season, scored his first power-play goal in the NHL with 3:29 left in the third period to snap a tie and lift the Kings to a 2-1 win over the Chicago Blackhawks.
Left open at the inside edge of the right circle, Weaver sent a shot past Chicago goalie Nikolai Khabibulin high on the glove side after taking a cross-ice pass from Alexander Frolov.
"I noticed they had a lot of their forwards down deep," Weaver said. "So I went backdoor. Frolov saw me and made a nice pass across and gave me some time to wind up."
"I'm usually not on the power play," he added. "I got some power-play time today and it was nice to get a goal."
The goal was Weaver's third this season. He scored his first NHL goal on Feb. 6 at Tampa Bay.
"It's funny, the first goal of my NHL career was a couple of weeks ago and all of a sudden now I have three, it's great."
Los Angeles coach Marc Crawford said he plans to give Weaver, in his second season with the Kings, more ice time.
"Mike is probably the one player that we've had this year that we didn't play enough early," Crawford said. "When he got his opportunity in early January, he's been good since then."
Patrick O'Sullivan had a goal and assist for the Kings, 4-1-1 in their past six games following a five-game losing streak.
Patrick Sharp also scored for Chicago, which dropped its fourth straight.
Los Angeles defenceman Rob Blake left the game after the first period with a strained neck and is day-to-day.
Kings goalie Mathieu Garon made 26 saves. Khabibulin stopped 30 shots.
Both the Kings and Blackhawks have been eliminated from playoff contention. Chicago will miss the post-season for the eighth time in the past nine seasons.
"Some guys are fighting for contracts and jobs," Chicago coach Denis Savard said. "The most important thing is to play for pride. You've got to have it night in, night out.
"In a game, if you've got six, seven guys not going it's tough. You can't play two lines all night long."
O'Sullivan, a rookie, extended his point streak to seven games. He has two goals and eight assists during the span.
"I know both teams aren't going to be in the playoffs, but these last few games of the regular season are important," O'Sullivan said. "It's kind of like our playoffs, so it's not surprising that the games have been physical."
Sharp scored for the third straight game and has seven goals in his past eight games.
O'Sullivan opened the scoring during a 5-on-3 power play midway through the first period, beating Khabibulin on the glove side with a shot from the low edge of the right circle.
Khabibulin had stopped a Kings' attack seconds earlier. The puck landed in the right corner, where Mike Cammelleri passed it to O'Sullivan.
Sharp tied it at 1 with a power-play goal at 6:10 of the second. He slipped past the Kings defence on right wing, broke in on Garon and fired a shot over his shoulder on the stick side.
Notes: Chicago RW Peter Bondra sat out his fourth game with a shoulder injury. Blackhawks C Jeff Hamilton missed Friday's game with a sore back. ... Los Angeles C Derek Armstrong missed his seventh game with a knee injury. Kings D Lubomir Visnovsky sat out with an undisclosed injury and LW Noah Clarke was a healthy scratch.