Regehr, who joined the defending Stanley Cup champions in a trade with Buffalo on Monday, played for coach Darryl Sutter while with Calgary during the 2003-04 season when the Flames came within one victory of winning the title.
"There was a little bit of nervous energy," Regehr said. "It's been a very busy last couple of days and lots of stuff going on, like getting to know new teammates.
"It was nice just to go out there and play. The guys played really hard. We had a great start and jumped on them early."
Regehr earned an assist on Williams' second goal. He also blocked two shots and was credited with a game-high six hits.
"He's exactly what we thought he was," Williams said. "He's a hard-nosed defenseman, he's hard to play against, and he's not going to give an inch to anyone on the opposite team. That's what we need, and we're all happy as forwards that he's with us now.
"I'm familiar with him from playing against him, and I really didn't care for it."
Williams extended his goal streak to five games, eclipsing his previous best. He picked up a loose puck along the boards in the Kings zone, after a long wrist shot from the right point by Mikko Koivu went wide, and carried it deep into the Minnesota end before putting a wrist shot past Niklas Backstrom's stick at 1:29.
"I know I've had a lot of shots this year, and I knew that if I kept them on the net, good things will happen," said Williams, who leads Los Angeles with 120 shots. "I've gotten some lucky ones during this little stretch here and I've had some good ones. I'm feeling better and I'm feeling a bit more confident that pucks are going to continue to go in."
Bernier made 23 saves en route to his sixth NHL shutout and first since Feb. 12, 2012 -- also against the Wild at Minnesota. The five-year veteran is 9-0 with a 1.50 goals-against average in 10 starts.
"I guess I've got a pretty good record against them (3-0-2), but it was actually a pretty easy game for me," Bernier said. "The guys did an awesome job in front of me, blocking a lot of shots and clearing those pucks. When you get two quick goals like that, it definitely helps the goalie."
Mike Richards set up the second goal with a pass deep in the right circle to Carter, who got behind Devin Setoguchi and slid his 21st goal through Backstrom's pads before many in the sellout crowd had found their seats.
Minnesota coach Mike Yeo replaced the six-year veteran with Darcy Kuemper, who faced only four shots the rest of the period.
It was the second time Backstrom was pulled from a game this season and the first since March 5, when he gave up four goals on 17 shots in the first period of a loss at Chicago. It was Kuemper's first appearance since that game.
"It's tough for sure to start the game like that," Yeo said. "We have to eliminate some of the big mistakes we are making. Two goals on line changes, that's usually something we are pretty strong on. This has been a grueling stretch, but we have a couple of days now and we have to use them the right way -- get the rest and get focused on this final stretch."
Williams made it 3-0 at 3:52 of the second with his 10th goal. He took a long lead pass at the red line from Anze Kopitar and beat Kuemper high to the glove side with a shot from the top of the right circle.
Minnesota lost on consecutive nights for the first time this season, slipping out of a first-place tie in the Northwest Division with Vancouver.
The Wild beat the Kings in a shootout on March 30 and will host them again April 23.
"We owed them," Williams said. "We had a 3-1 lead in their building and let them come back. We had them on a back-to-back then and we had them on a back-to-back tonight also. But this time we didn't let them back in the game, mostly because of Bernier's play.
"I thought we got a little bit sloppy in the second period and toward the end of the first, but I thought we finished the game well."
Minnesota forward Jason Pominville, who was teammates with Regehr with the Buffalo Sabres before they were traded two days apart this week, also played his first game with his new team.
"We had some good (offensive) zone time, and I think the scoring chances will definitely come for sure," Pominville said. "I think we can find ways to create a little bit more."
The Kings, who had just 14 shots, returned from a 3-1-1 trip.
Wild LW Dany Heatley (injured wrist) was scratched for the first time this season. He was injured during an altercation with San Jose's Marc-Edouard Vlasic at the end of Wednesday night's 4-2 loss. ... Williams has had two four-game goal streaks during his 12-year career. ... All 11 of Kopitar's points on the power play have been assists. Six of Carter's seven points on the power play have been goals. ... Minnesota has allowed the first goal in five straight games, after scoring first in 10 of its previous 11.
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LOS ANGELES, CA - APRIL 04: Newly acquired forward Jason Pominville #29 of the Minnesota Wild skates during...