Next best during that span is the Chicago Blackhawks at 20-11.
"We know our game plan and the key thing is possession," Kings forward Tanner Pearson said. "That's the most important thing. If you lose that first faceoff, get that puck back as quick as possible and not lose your coverage."
The Kings usually start overtime with two above-average faceoff men in Anze Kopitar (52.5 percent) and Carter (53.1), and defenseman Drew Doughty.
Carter has three overtime goals in 45 games this season after scoring three overtime goals in 77 games last season. Kopitar scored four overtime goals last season.
Video: WPG@LAK: Muzzin feeds Carter for game-winner in OT
The group coach Darryl Sutter often uses next also has gotten the job done: Defenseman Alec Martinez (three overtime goals since the start of 2015-16), Pearson (four) and forward Tyler Toffoli (one), though Toffoli last played Dec. 20 because of a lower-body injury.
The Kings play to their strengths.
"When you look at it, there's more room on the ice," Pearson said. "A lot easier to lose guys. [The overtime games] could have gone either way. For us, it's gone the right way. We've just got to keep on doing it."
Martinez, who had one overtime goal last season and two this season, believes the exceptional run has been fed, in part, by its own success.
"Maybe a sense of confidence," Martinez said. "It's just one of those things where it's no different than any other time of the game or situation. The more you play in it, the more comfortable you get.
"When you've got a guy like Pearson, or earlier in the year when [Toffoli] wasn't injured, if you have a hard time playing with those two, it's probably you. It's not them. I just try to get it in their hands and they do the work."
Since 3-on-3 overtime play began, there has been no month of regular-season play when the Kings haven't won a game in overtime.
They have defeated the Nashville Predators three times in overtime, and the Minnesota Wild, Chicago Blackhawks, Columbus Blue Jackets, San Jose Sharks, Pittsburgh Penguins and New York Rangers twice each.
Video: MIN@LAK: Pearson deflects OT winner past Kuemper
In their 25 games decided in overtime since October 2015, the Kings have lost to the Buffalo Sabres, St. Louis Blues and New Jersey Devils (last season) and the Dallas Stars (this season, Dec. 23) during this run.
It is also a noticeable turnaround from the final season of 4-on-4 overtime, 2014-15, when the Kings were 1-7 in and missed the Stanley Cup Playoffs, mainly because their record beyond 60 minutes (overtime and shootouts) was a combined 3-15.
Focus on the future
Regenerating a winning atmosphere with the Arizona Coyotes is a process rookie forward Brendan Perlini says is a focus every day.
Perlini, 20, was the No. 12 pick in the 2014 NHL Draft. He made his NHL debut Dec. 5, scored his first goal in his fourth game, Dec. 10 against the Predators, and has six goals in 19 games.
"We started off great this year in Tucson [American Hockey League] and it was great to get that winning feeling," Perlini said. "Here I keep the same attitude, and although we're not winning I know what I have to do to learn. Being a bit selfish, I'm trying to learn what I can from the older players but it's been tough when we're not winning. But you're in the NHL. You can have fun coming to the rink every day while you're learning and trying to get better."
Perlini has scoring in his genes. His father, Fred Perlini, was an eighth-round pick (No. 158) of the Toronto Maple Leafs in the 1980 NHL Draft. He played eight NHL games and spent 11 seasons in the British Hockey League, where he scored more than 100 goals in a season three times.
Brendan was born in Guildford, England in 1996, before Fred played his final season, 1996-97, with the Guildford Flames.
When Brendan Perlini was called up to the NHL, he was tied for the AHL lead with 11 goals. He had a six-game goal streak Nov. 5-27, the longest by a rookie in the AHL since Tyler Johnson, now with the Tampa Bay Lightning, had goals in nine straight for Norfolk from March 3-24, 2012.
Video: WPG@ARI: Perlini snaps a quick shot past Hellebuyck
When the Coyotes went on their five-day break Jan. 8-12, Perlini was reassigned to Tucson, and in his first game had a hat trick against Manitoba on Jan. 10.
He returned to the Coyotes and scored two against Manitoba's parent team, the Winnipeg Jets, on Jan. 13.
"Going to Tucson was a good thing," Perlini said. "There are so many good players up here that, especially being a young guy, you don't get the minutes. So I went and played lots and you gain a lot of confidence from that."
Veteran referee Tom Kowal will work his 1,000th NHL regular-season game Thursday in Calgary. … Among goalies who have played at least 16 games this season, the Calgary Flames' Chad Johnson has cracked the top 10 in save percentage at .923, and the top eight in goals-against average, at 2.24. He's 16-10-1 in 27 games. … Vancouver Canucks captain Henrik Sedin is one point from 1,000 in his NHL career. Sedin will be the 85th player, seventh active player and first from the Canucks to reach the milestone. … One of those active players is Joe Thornton of the San Jose Sharks. Thornton had two assists Wednesday to move him past Johnny Bucyk for 24th all-time with 1,370 points. He has three goals in 44 games this season, and all three have been scored into an empty net. … After the Coyotes had their five-day break, they had five games in seven days. "We're young enough and we've got lots of energy," coach Dave Tippett said of the busy week. … Edmonton Oilers forward Patrick Maroon, who has been getting regular left-wing duty with center Connor McDavid, is tied for first in the League with seven goals in January; Brad Marchand of the Boston Bruins also has seven goals this month. … Los Angeles Kings coach Darryl Sutter had his 617th win as an NHL coach, against the Winnipeg Jets on Jan. 14, tying him with Jacques Lemaire for 12th in coaching victories. Bryan Murray is 11th with 620 wins.
Video: PHI@BOS: Marchand finishes off five-point game
Games to watch
Edmonton Oilers at Calgary Flames (Jan. 21, 10 p.m. ET; SN, CBC, NHL.TV)
The Battle of Alberta resumes at Scotiabank Saddledome. It's the fourth and final regular-season game between the teams this season. Edmonton has won the previous three, including 2-1 in a shootout in Edmonton on Saturday.
Los Angeles Kings at New York Rangers (Jan 23, 7 p.m. ET; TVA Sports, SN, SN1, MSG, FS-W, NHL.TV)
It's the second game of a four-game trip for the Kings, who will be into their final scheduling challenge of the season. With the game at Madison Square Garden, they will have started a stretch of nine of 10 away from home, with all but one of those road games against Eastern Conference opponents. After the stretch, the Kings will have 10 road and 17 home games remaining.
Calgary Flames at Montreal Canadiens (Jan. 24, 7:30 p.m. ET; RDS, SNE, SNW, NHL.TV)
The Flames make their annual visit to the Bell Centre as the middle game of a three-game trip at Canada's three Eastern Conference teams, the Maple Leafs, Canadiens and Ottawa Senators.
Edmonton Oilers at Anaheim Ducks (Jan. 25, 10 p.m. ET; PRIME, SNW, NHL.TV)
The Oilers start a back-to-back right before the 2017 Honda NHL All-Star Weekend, and it's shaping up as another battle of Pacific Division contenders. The last time Edmonton faced Anaheim, Oilers forward Leon Draisaitl scored in overtime for a 3-2 victory on Dec. 3.
Edmonton Oilers at San Jose Sharks (Jan. 26, 10:30 p.m. ET; CSN-CA, SNW, NHL.TV)
The top spot in the Pacific Division could be at stake at SAP Center when the Oilers visit the Sharks for the second time this season. The last time they played in San Jose, the Sharks won 3-2 in overtime on a goal by Kevin Labanc on Dec. 23.
-- NHL Staff Writer Lisa Dillman contributed to this report.