Jonathan Quick made 22 saves and Jarret Stoll also scored for Los Angeles, which would have fallen into a tie for eighth with Detroit had it lost in regulation. Instead, the Kings took a two-point lead over the Red Wings, who lost a shootout of their own in Dallas.
"We just found a way to win," Brown said. "Over the course of the year there are many up-and-down games that maybe we should or should not have won. I think it all evens out in the end. It's just a matter of being consistent. The points are so important right now with Detroit right behind us. And today was one of the games that, once we're in the playoffs, we will say was huge."
The Bruins grabbed a 3-1 lead after 40 minutes as Blake Wheeler and Michael Ryder scored 11 seconds apart during the second period. Miroslav Satan also scored and Tim Thomas made 21 saves for Boston, which got defenseman Mark Stuart and forward David Krejci back in the lineup but remains without top centers Marc Savard and Patrice Bergeron.
"We were very shorthanded, I'll be honest. But it was positive overall," Thomas said, talking about a California road trip in which the Bruins captured three of a possible six points. "Even though the bite of not getting the two points might not feel good, if you look at the big picture, it was a good trip. We very easily could have came out with six out of six points."
Quick helped spark his team's comeback when he stopped Daniel Paille on a shorthanded breakaway late in the second that could have given the Bruins a 4-1 lead.
Instead, the Kings cut the deficit to one when Brown converted an Alexander Frolov feed with 9:28 left in regulation and tied the score on a Kopitar goal with 7:06 remaining. The play was set up when Michal Handzus worked the puck free along the right wall and got it to Wayne Simmonds behind the net. Simmonds found Kopitar in front for the score.
"It was our mindset that made the difference. Everyone got pretty hyped up, the crowd loved it, and we feasted off of it," Kopitar said. "We built some momentum and we were able to get some late goals. That extra point is very big right now."
The opening faceoff came shortly after 1 p.m. Pacific time, marking the fifth Saturday afternoon home game for the Kings this season. They started 0-2-1 before beating Washington 2-1 two weeks ago, and got off to a good start against Boston when Stoll tapped in the rebound of a Scott Parse shot at 11:42 of the first period.
But the Bruins began to take control after that. First, Satan scored his second goal in six games since signing as an unrestricted free agent. His wrist shot from the top of the right circle beat Quick to the glove side with 1:40 left in the first, tying the score.
Then, in the blink of an eye, that tie became a 3-1 lead for the visitors midway through the second. Wheeler took a sharp-angled wrist shot that caromed off Quick's pads before deflecting into the net off his own defenseman, Sean O'Donnell, at 10:53.
If the Kings were momentarily stunned, the Bruins took full advantage. They won the ensuing faceoff, stormed up ice and put another puck past Quick, as Ryder finished off Wheeler's backhanded centering pass.
"Our guys left it all on the ice again today," Boston coach Claude Julien said. "It's unfortunate that we weren't able to come up with the win."
Material from wire services was used in this report