The second goal of the night for the 35-year-old Gaborik gave him 400 for his career. It came off an assist from Kopitar, his 500th in the NHL.
"They were asking me, who gets the puck?" Kings coach John Stevens said.
"I'm happy for those guys. Kopi's just been a horse all year. It's impressive to me to see that type of number with Gabby at his age and the injuries he's fought through, to be that good a player. That's kind of fitting that those two guys would partner up on a milestone like that."
The Kings are the NHL's best third-period team, so their onslaught hardly came as a surprise to the Wild.
"You knew they're plus-23 in the third and leading the league in that," coach Bruce Boudreau said. "When they put their push on, we just didn't do anything about it."
The Kings are now plus-27 in the third.
"That was probably as good a third period as we've had this year," Stevens said.
Kopitar added an empty-net goal to go with his two assists. He has 15 goals this season.
"We were just able to lock the game down," Kopitar said. "They didn't have much in the third, and I think we did a good job."
The Wild played well enough in the first two periods to carry a 2-1 lead into the third.
Los Angeles tied it on a 2-on-1 breakaway, with Kopitar giving Gaborik a late feed for his first goal.
"You don't want to give them life or anything to feel good about," Dubnyk said. "The 2-on-1 from the far blue line, obviously they made a nice play. They're feeling good, the energy in the building is high and they start coming back. That's a good hockey team."
The Kings took a 3-2 lead on a fluke goal. Kempe fired a shot that was blocked by Dubnyk, but the deflection went off the skate of Minnesota's Jonas Brodin and into the net.
"If we hadn't touched the puck, it's going into the corner," Boudreau said. "To me, that's frustrating."
Gaborik's milestone goal also had some assistance. Taking another pass from Kopitar after a faceoff, his shot deflected off the stick of Minnesota's Matt Dumba and then the near post before hitting the net.
Boudreau said there was interference on the play that the officials failed to call.
The Wild coach also thought his team was lacking something.
"They don't have that self-confidence that I think we had last year," he said. "When our third periods came, they just knew they were going to win. Now every game has been a battle."
The Kings remain undefeated in regulation when scoring three-plus goals (14-0-2). . Gaborik did not start on the first line with Kopitar, but was switched late in the second period. "I'm getting more comfortable with each game. Obviously the lines change, but it's a long season. Whatever it takes to win games. Tonight it clicked pretty well for us," Gaborik said. ... Minnesota had won four of six.
Wild: Head down the freeway to play Anaheim on Thursday.
Kings: Remain home to host Ottawa on Thursday.
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This story has been corrected to Kings hosting Ottawa on Thursday.