Gaborik, who scored the first goal in Wild history and remains the franchise leader in several categories, finished a two-on-one with Anze Kopitar to tie the score 2-2 at 4:35 of the third period.
After Adrian Kempe put Los Angeles in front at 12:38, Gaborik made it 4-2 with six minutes left when he shot through traffic and the puck went off the stick of Wild defenseman Matt Dumba and past goaltender Devan Dubnyk.
Kopitar received his second assist on the play, the 500th of his career, and he scored an empty-net goal with 56 seconds left.
Kempe put the Kings on top when he tossed the puck toward the Minnesota goal from the sidewall. Dubnyk poked the puck away, but it went off the skate of Wild defenseman Jonas Brodin and back across the goal line.
Jake Muzzin had a goal and an assist, Drew Doughty had three assists and Jonathan Quick made 19 saves for Los Angeles (18-8-3).
Charlie Coyle and Tyler Ennis scored and Dubnyk made 23 saves for Minnesota (13-11-3).
After neither team scored the first 30 minutes, the Wild and Kings combined for three goals in a 4:04 span of the second period.
Coyle gave Minnesota a 1-0 lead when he redirected a pass from Chris Stewart at 10:30.
The Kings tied the score at 14:24 when Doughty passed from the top of the right circle to his partner at the top of the left circle, and Muzzin scored on a hard slap shot for his third of the season.
The Wild quickly regained the lead at 2-1 when Ennis took the puck from behind the Wild net and slapped in his own rebound at 15:34.
NOTES: Wild G Devan Dubnyk came in 7-4-1 in his career against the Kings with a .931 save-percentage and 2.29 goals-against average, better than his .916 and 2.55 career marks. ... Minnesota C Charlie Coyle has a five-game point streak (one goal, four assists). ... Kings LW Marian Gaborik has eight points (five goals, three assists) in 12 career games against Minnesota. ... Los Angeles came in with the top penalty-kill unit in the NHL at 89.5 percent, and the Kings thwarted the Wild's lone power play. ... Kings C Andy Andreoff, who has been sidelined since getting knocked down by a punch from Anaheim Ducks D Kevin Bieksa on Nov. 25, has been cleared to resume practicing. ... Kings C Torrey Mitchell went 6-0 on faceoffs.