Phil Kessel and Darryl Boyce scored 34 seconds apart in the second period for the Maple Leafs, who reached the midway point of their season with three straight wins. Toronto hasn't lost on the road since Dec. 18.
"I thought we played a very good road game," Leafs coach Ron Wilson said. "We got down early, but we weren't frustrated or anything. We got our game going in the second period. The 'D' started moving pucks and jumped into the play. Each line scored a goal, so it was huge for us."
Wayne Simmonds and Michal Handzus scored for the Kings, who have lost six of seven -- including five of six on their current eight-game homestand.
Jonathan Quick stopped 25 shots, but the Kings missed several chances to tie it in the final minutes, including a 6-on-4 advantage in the final 1:42.
"When you're playing a team that you don't see a lot, you try to focus on the things that you have to do," Kings defenseman Rob Scuderi said. "I think we did a good job of that in the first period and in the last 15 minutes, but it's not enough. We find a way to do just enough to lose by one goal. That's been the case since Christmas, and it's got to turn around for us."
Kulemin put the Leafs ahead with a nifty spin and a short shot past Quick after the Kings broke down defensively. With an assist from linemate Mikhail Grabovski, the goal was the third in two games for Kulemin, who leads the Leafs with four game-winning goals.
After Phaneuf took a late slashing penalty, Los Angeles got the puck behind Reimer with 35 seconds left, but video review confirmed it didn't cross the goal line.
Colby Armstrong had an assist while starting at center for the Maple Leafs just three days after the cornea in his right eye was scratched by a sucker-punch from Atlanta's Ben Eager.
Staples Center was filled with hundreds of blue-jerseyed fans for Toronto's first visit to Los Angeles since December 2008.
The Kings took a 1-0 lead late in the first period when Simmonds got the puck in the corner and skated past Toronto captain Dion Phaneuf to the net, scoring his first goal since Dec. 26 and his first point in eight games.
Toronto evened it early in the second period when Boyce got a 1-on-1 break against Kings defenseman Alec Martinez. Boyce's exceptional shot went between Martinez's legs and into the glove-side corner of Los Angeles' net for his second goal in six games since joining the Leafs on Dec. 30.
One shift later, Joey Crabb's pass through the slot went past Scuderi and Drew Doughty to Kessel, who scored his team-leading 18th goal. Los Angeles tied it late in the second period on the sixth goal by Handzus.
"They came hard with a lot of pressure, dumping pucks in, but kudos to the guys," Reimer said. "The team that's down is always going to push hard. I just tried to take it shot by shot and not look at the clock."
The Kings began the second half of their season in a tie for ninth place in the Western Conference -- not exactly where they hoped to be after leading the overall NHL standings earlier this fall. Los Angeles held a brief players-only meeting after the game.
"It's something that needs to be changed with our attitude," captain Dustin Brown said. "That's all it is, really - playing the game right. We're halfway through the year, this is a big homestand for us, and the playoffs are at stake, so we've got to find a way to get it going. We need to look each other in the face and get this thing turned around. I'm not sure what we need to do, but we'll figure it out as players."
Material from wire services and team media was used in this report.