Kopitar and Williams each added a goal and two assists to lead the Kings. The trio, which has clicked for 18 points (7 goals, 11 assists) in the first three games of the season, quickly helped Los Angeles build a three-goal lead in the first period.
Teddy Purcell and Smyth scored to overcome a late rally by the Wild, who had drawn within 4-3 on a goal by Kim Johnsson 6:24 into the final period.
"That top line carried us tonight for sure," said Kings defenseman Jack Johnson, who assisted on Smyth's first goal. "When your best players are playing well there is a good chance you are going to win."
Michal Handzus also scored for the Kings (2-1) and Jonathan Quick made 26 saves as Los Angeles completed its season-opening three-game homestand.
Coupled with a 6-4 victory over San Jose on Tuesday, the Kings have scored six goals in consecutive games for the first time since November 1997.
"The big thing is that we're communicating in practice and obviously it's leading out into the game situation," said Smyth, acquired in a trade with Colorado this summer. "It's a good mix and things are going good right now."
Martin Havlat and Nick Schultz had power-play goals for the Wild, who were playing the first game of an 11-day, five-game trip. Josh Harding made 17 saves for Minnesota in his first appearance of the season. He gave up goals on two of the first three shots he faced.
"We had some guys who just weren't ready for the start of the game," Minnesota coach Todd Richards said. "And you're not going to win a lot of games if you're starting second periods down by three goals."
The Wild had rallied from a 3-0 third-period deficit to beat Anaheim 4-3 in overtime, and found themselves in a similar situation Thursday.
With the Kings continuing to struggle killing penalties -- giving up seven goals in 11 power plays -- Minnesota got back into the game.
"Our decision-making hasn't been great, and down 3-0, we're lucky to come back once and it's tough to do every night," Wild forward Andrew Brunette said.
Los Angeles had the worst 5-on-5 offense in the NHL last season (214 goals), but with an emphasis on attacking the net, the Kings have seven full-strength goals in two games.
"It takes a couple of veterans like Ryan Smyth to set the example," Los Angeles coach Terry Murray said. "It's only three games in, but you can see some of the stuff he brings. The younger guys are watching and doing the same."
Smyth tipped in a shot by Johnson, giving the Kings a 1-0 lead 67 seconds into the game. Williams deflected a shot by Drew Doughty under Harding just over 2 minutes later.
Kopitar finished a sharp 2-on-1 break with Smyth midway through the period for his third goal of the season, making it 3-0.
The Wild converted on their first power-play opportunity, as Havlat one-timed a shot from the slot past Quick 22 seconds after Sean O'Donnell was called for interference.
Handzus beat Harding with a shot from the left circle to restore Los Angeles' three-goal lead at 11:02 of the second. But Schultz lifted a backhander past Quick during a power play 4 minutes later. It was Schultz's first power-play since Jan. 17, 2004.
O'Donnell played his first game of the season after completing a five-game suspension that carried over from an altercation during the preseason. ... Minnesota F Pierre-Marc Bouchard missed a second game while being evaluated for a possible concussion. ... The Kings start a six-game trip at St. Louis on Saturday.
Copyright by STATS LLC and The Associated Press
Arena: STAPLES Center Location: Los Angeles, California
Referees: David Banfield, Tom Kowal Linesmen: Jonny Murray, Mark Wheler
Attendance: 14,995 (82.8% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Ryan Smyth (2)
Assists: Jack Johnson, Rob Scuderi
Justin Williams (1)
Assists: Drew Doughty, Anze Kopitar
Anze Kopitar (3)
Assists: Ryan Smyth, Justin Williams
Martin Havlat (1)
(Power Play) Assists: Andrew Brunette, Mikko Koivu
Michal Handzus (1)
Assists: Alexander Frolov, Wayne Simmonds
Nick Schultz (1)
(Power Play) Assists: Eric Belanger, Owen Nolan
Kim Johnsson (1)
Assists: Antti Miettinen, Benoit Pouliot
Teddy Purcell (2)
Assists: Jarret Stoll, Dustin Brown
Ryan Smyth (3)
(Power Play) Assists: Anze Kopitar, Justin Williams