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.
Jamie Lundmark and Brian Willsie scored less than 3½ minutes apart to erase an early two-goal deficit, and Scott Thornton also had a goal for the Kings, who have an NHL-worst 14 losses after regulation.
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.
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 four 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.
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.
Lundmark scored just 29 seconds later from the edge of the crease. It was Lundmark's fifth goal this 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.
Notes: The Stanley Cup was in the building, part of a charity event sponsored by actress/model Carmen Electra to help raise money for brain tumour 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's 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.