Alexeev and Denis Arkhipov scored first-period goals for the Blackhawks, who have won four of five -- including two in shootouts. Nikolai Khabibulin made 24 saves.
"We jumped to a quick lead in the first, and then they scored three times on us. That was discouraging, and we talked about it during the second intermission," Khabibulin said. "We said if we could stick to the system, skate with them and forecheck a little harder, we would have a chance to come back and win the game."
Jamie Lundmark and Brian Willsie scored less than 3 1/2 minutes apart to erase an early two-goal deficit, and Scott Thornton also had a goal for the Kings, who have lost more games after regulation than anyone else.
"We've been in a lot of games and we've gotten some great goaltending that's given a chance to win every night," Thornton said. "We obviously want to be competing every night, and since Christmas I think we've done a great job of doing that. We've obviously been at the bottom of the playoff race for a long time, but the good thing about our locker room is that the guys have a good attitude."
Ruutu tied it with 8:07 left in regulation, carrying the puck out from behind the net and putting a backhander past goalie Sean Burke's left skate for his 16th goal. It was one of only three shots by Chicago in the third period -- one fewer than the Kings.
"Three of the last five games we've had a one-goal lead going into the third period and lost the game, so we've got to get that killer instinct," Los Angeles defenseman Aaron Miller said. "There is a difference between being close and winning games, and we have to try and figure that out."
Willsie, who turns 29 on Friday, tied the score 2-all at 17:11 of the first period while Arkhipov was serving a holding penalty.
Thornton put the Kings ahead 3-2 at 15:36 of the second, just 4 seconds after the Blackhawks killed off Patrick Sharp's tripping penalty. Tom Kostopoulos carried the puck deep in the right circle and waited for Khabibulin to commit before setting up Thornton's sixth goal with a perfect cross-ice pass.
"I guess after a while you start thinking about it, but scoring goals is not my major function on the team," Thornton said after ending a 16-game drought. "I can't say enough about the way Kostopoulos and Willsie have been playing, and we've been clicking as a line. It's been a lot of fun the last five or six games."
Alexeev opened the scoring at 4:54 of the first period with his 11th goal. The Blackhawks didn't record another shot on net until Adrian Aucoin was stopped on a wrist shot from the right point and Arkhipov converted the rebound at 13:21 for his ninth of the season and first in 18 games against the Kings.
"Alexeev and Arkhipov played a heck of a game for us," Chicago coach Denis Savard said. "Overall I'm pleased with everybody. It's tough to win on the road."
Lundmark scored just 29 seconds after Arkhipov's goal. It was his fifth of the season and fourth in 19 games since joining the Kings on Jan. 29.
The Blackhawks entered with the NHL's worst power-play percentage (12.1), and the Kings came in with the league's lowest penalty-killing percentage (77.5). Chicago was 0-for-4 with the man advantage, including one in overtime after Rob Blake took a hooking penalty.
The Stanley Cup was in the building, part of a charity event sponsored by actress/model Carmen Electra to help raise money for brain tumor survivors and their families. ... Of the 96 NHL players who have at least 20 goals this season, only Chicago RW Martin Havlat (24 goals) and Calgary LW Alex Tanguay (20) have not scored a game-winner. ... The Kings have 20 power-play goals in 20 games. Until Willsie's goal, they were the only Western Conference team that hadn't scored against the Blackhawks with the man advantage.
Copyright by STATS LLC and The Associated Press
Arena: STAPLES Center Location: Los Angeles, California
Referees: Tom Kowal, Rob Martell Linesmen: Shane Heyer, Brad Lazarowich
Attendance: 16,110 (88.9% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Nikita Alexeev (11)
Assists: Denis Arkhipov, Danny Richmond
Denis Arkhipov (9)
Assists: Adrian Aucoin, Martin Lapointe
Jamie Lundmark (5)
Assists: Raitis Ivanans, Dustin Brown
Brian Willsie (10)
(Power Play) Assists: Patrick O'Sullivan, Jaroslav Modry
Scott Thornton (6)
Assists: Tom Kostopoulos, Jamie Heward