Captain Anze Kopitar scored a first-period goal that made him the Kings’ leading scorer for the 15th time in the last 16 seasons, while Kempe and Trevor Moore scored 49 seconds apart in the second period.

Kempe completed his fourth career hat trick on an empty-net goal with 1:39 to play, and dozens of visiting Kings fans littered the ice in celebration. With 41 goals, Kempe is the first Kings player to reach the 40-goal mark since Luc Robitaille in 1993-94.

Roughly 40 minutes after leaving the ice, the Kings learned they’ll face the Edmonton Oilers in the first round of the playoffs for the second consecutive season. The best-of-seven series starts Monday in Edmonton.

Shaking off a 2-5-0 skid that scuttled their chances at the division title, the Kings won their final two games to finish with 104 points, the second most in franchise history behind the 1974-75 squad (105).

“It’s nice to have the feeling of positive morale, positive momentum going into (the playoffs),” Kings defenseman Mikey Anderson said. “We’ve found some ways to score goals and had a couple of physical games as well, so that’s all been good for us.”

Troy Terry, Max Jones and Trevor Zegras scored for the Ducks, who wrapped up one of the worst NHL seasons of the 21st century on a 13-game winless streak. Coach Dallas Eakins’ contract is finished after his fourth consecutive losing season, but the rebuilding Ducks have made no announcement about his future.

“There’s a number of things that we’re very proud of,” Eakins said. “I am proud that in a game like this where it’s our last game, we know it’s totally over, that they still had some rage in them. I thought they went out and battled hard and really kept the love of the rivalry between us and the Kings.”

The Ducks’ silver lining on their NHL-low 58 points is the best chance in next month’s draft lottery to win the right to select Connor Bedard, the Regina Pats center considered the most tantalizing prospect since Connor McDavid.

Kings and Ducks players scuffle near the Ducks’ bench during the third period Thursday.

(Ashley Landis / Associated Press)

The Ducks will have only a 25.5% chance of securing its first No. 1 pick in the NHL draft. But they can fall no lower than third in the lottery, which means they will get a premium prospect in a top-heavy field headlined by forwards Bedard, Adam Fantilli and Matvei Michkov.

Joonas Korpisalo made 21 saves for the Kings, and John Gibson stopped 31 shots for the Ducks.

“It’s never easy losing games like that,” Ducks defenseman Cam Fowler said. “We’re all competitive people and want to do well, but I think I’m proud of the way we stuck together. We never cracked as a team and continued to support one another.”

The Ducks missed the playoffs for the fifth consecutive season, extending the longest drought in their history for a team that had never missed more than three straight postseasons. The Ducks had a pathetic season by nearly every measure, ranking last in the NHL in goal differential (minus-129) and goals allowed while ranking 31st in goals scored (209).

Statistically, the Ducks were the worst defensive team of the past quarter-century. Their 338 goals allowed were the most by any NHL team in the past 26 seasons since the 1995-96 San Jose Sharks gave up 357, while their goal differential was the NHL’s worst since the 1999-2000 Atlanta Thrashers (minus-143).

The Ducks’ players have been justifiably uninterested in their team’s draft lottery status as their season limped on, and Terry underlined that stance by scoring just 2:44 into the season finale.

But the Kings evened it late in the first period when Kopitar knocked down a high puck from Kempe and scored his 28th goal of the season. In the second, Kempe got a delayed goal after video review, and Moore scored moments later on a two-man rush.

Zegras scored his 23rd goal with 5:09 to play, trimming the Kings’ lead to 4-3. After a lengthy dust-up, Kempe finished off the victory.

Kevin Fiala sat out his sixth consecutive game for the Kings because of a lower-body injury. The playoff availability of the team’s high-scoring Swiss forward is unclear, but Kopitar used the final game to break his tie with Fiala atop the team’s scoring leaderboard.

Defenseman Alexander Edler and forward Gabe Vilardi also remained out of the Kings’ lineup with injuries.

Mason McTavish sat out for the Ducks because of an upper-body injury, finishing his rookie season with 43 points in 80 games.

Up next for the Kings: at Edmonton on Monday night in the first round of the playoffs.