Carter tied it 1-1 with three seconds remaining in the first when he crashed the net and backhanded in the rebound of a shot by Kopitar off a face-off.
Andreas Athanasiou, who was making his Kings debut, got the rebound of Carter's initial shot off the pad of Talbot during a 4-on-4 to give Los Angeles a 2-1 lead at 7:12 of the second period.
"[Carter is] a utility guy for us. Put him in any situation he will deliver," Kopitar said.
Brown extended the lead to 3-1 at 17:05 when his pass from behind the net redirected in off Carson Soucy's skate on the power play. Brown is the sixth Kings player to score at least 300 goals, joining Luc Robitaille (557), Marcel Dionne (550), Dave Taylor (431), Kopitar (333) and Bernie Nicholls (327).
NOTES: Kaprizov is the third player in NHL history to score an overtime goal in his debut, joining Nick Knott (1941-42 with the Brooklyn Americans) and Tim Sweeney (1990-91 with the Calgary Flames). … Forwards Nick Bonino, Marcus Johansson and Nick Bjugstad made their debut with the Wild. Bonino was 13-for-20 on face-offs, Johansson had one hit in 17:29 of ice time, and Bjugstad had one shot and one hit in 13:27. … Los Angeles and Minnesota will play again at Staples Center on Saturday.