"What do we have to lose, right? [Coach John Tortorella] just told to have fun and go play and what the [heck]," said Richardson, who signed with the Canucks as a free agent last summer after being released by the Kings.
"It's nice to beat those guys for sure."
It was Vancouver's first win against Los Angeles in five games this season (0-3-1).
Richardson finished it off into a wide-open net after Zack Kassian collected a rebound in the slot and drew two defenders to him before sliding it across to Richardson.
"Good vision lately," Richardson said of Kassian, who has six assists and eight points his past six games. "He would have screamed at me if I didn't get that one. It was an empty net."
Edler had an assist on the game-winning goal, and Eddie Lack made 25 saves in his 18th straight start, one short of the Canucks rookie record, to help Vancouver snap a three-game losing streak and stay in the playoff mix.
Vancouver is six points behind the Dallas Stars, who hold the second wild-card spot in the Western Conference. The Canucks have four games left, and the Stars have five remaining.
Slava Voynov scored a power-play goal with 28 seconds left in the second period to put Los Angeles up 1-0, but the lead didn't last long.
Jonathan Quick made 38 saves for Los Angeles, which has lost two straight since clinching a playoff berth and third place in the Pacific Division on Wednesday.
After blowing a lead in the second period of a 2-1 loss to the San Jose Sharks on Thursday, the Kings failed to close out a lead after two periods for the third time this season (26-3-0) Saturday night.
"It's frustrating," said defenseman Matt Greene, who returned after sustaining a cut to his right leg midway through the third period. "We've got to start locking it down. It's two third periods in a row. We had a lead in San Jose the other night too, and we've got to be able to lock these down going into the third period and win those games."
The Kings were called for three penalties in the first half of the third period, when they were outshot 20-7.
"We were short a couple guys on the back, and the penalties in the third took a little steam out of us," Kings coach Darryl Sutter said. "And then Greene going down."
Greene went to the locker room with 7:44 left in the third period. He returned to the bench with three minutes left in the game.
Greene said he sustained the cut to his shin when he blocked a shot from Jason Garrison.
"Just a pressure cut. It's fine," Greene said. "It happens."
After a good start, Quick made several great saves with the Canucks pressing late in the first period, swallowing up Shawn Matthias' shot from in front and kicking out his left pad to deny Garrison on a hard one-timer from the high slot. Quick's best stop came with four minutes left, sliding left to right to deny Vancouver captain Henrik Sedin, who returned after missing four games with a left-knee injury, on a backdoor pass.
Quick was called for unsportsmanlike conduct when he smashed his stick after getting stranded atop his crease on Richardson's goal, leaving the Kings shorthanded for the final 93 seconds. But Sutter wasn't upset his goalie eliminated the chance to play with an extra attacker late.
"It happens so rarely, it wasn't that big a deal," Sutter said.
Lack matched Quick's first-period robbery of Henrik Sedin with a similar backdoor stop on Kings rookie Tyler Toffoli on a 2-on-1 pass from Jeff Carter 45 seconds into the second period, but Voynov opened the scoring on a power play late in the period.
Four Canucks got caught below the goal line, leaving the Los Angeles defenseman alone inside the left hash mark for a passout by Carter. Voynov wristed a quick shot over a charging Lack and just under the cross bar for his first goal since Nov. 14, a span of 60 games.
"We just make a terrible coverage mistake on our penalty kill," Tortorella said. "We just talked about the first few shifts of just trying to gain momentum and not sink because we got scored on late. Then we score a power-play goal. I thought we played well."
Edler tied it on a power play 1:06 into the third period, pinching down from the point to deflect a cross-ice pass from Daniel Sedin past a helpless Quick. The goal was reviewed because the puck hit Edler's stick and skate before going in, but the call on the ice stood up because there was no distinct kicking motion.
"We have to bear down," Kings forward Marian Gaborik said. "We took three penalties, and they scored. We can't have breakdowns in our zone. We have to get ready and make sure it doesn't happen. We're heading into playoffs. These game situations can cost us big, so we have to figure it out."