Marian Gaborik scored with seven seconds left in regulation to force overtime, and then scored 12:07 into the extra period to lift the Kings to a 3-2 victory Saturday night.
Wresting home-ice advantage from the Ducks comes after the Kings staged a memorable comeback against San Jose, becoming the fourth NHL team to win a best-of-seven series after losing the first three games.
''It was awesome. Really, it was what you expect,'' Kings coach Darryl Sutter said. ''It was a physical game. I think the crowd really responded to that.''
''We did a good job on the forecheck,'' Gaborik said. ''The puck got to Kopi, he saw me driving to the net, and made a nice play. I just tried to tip it in.''
Gaborik ''is a big reason that we won the first round, and if he hadn't finished some of those opportunities it would have only gone six,'' Sutter said. ''If you look at both those goals, those are classic goals. You got to go to the net to score in the playoffs.
''Doesn't matter if we pull the goalie, still got to go to the net. Not many guys can score those goals, but you still got to go to the net.''
Hiller said the Kings ''suddenly had a 2-on-1 out of nowhere. It was a shot-pass that went off the post and off my back and in. It's too bad. We had a couple chances in OT to finish it, but at the end it's still a 1-0 series. We need to focus on the next game and learn from this. We have room for improvement.''
The Ducks and their fans - who got to chant ''Beat LA!'' for the first time in the postseason - appeared poised for a win after 43-year-old Teemu Selanne beat Jonathan Quick between the pads for a go-ahead goal with 11:52 to play in regulation. It was the first goal and fourth point of the playoffs for the Finnish Flash, who plans to retire at season's end.
But the Kings pulled Quick for a sixth attacker with 1:22 left. In the closing seconds, Mike Richards took a shot from along the left boards, and Gaborik wristed the rebound past Hiller, who slumped in the net after giving up the tying goal.
''They just threw it at the net,'' Hiller said. ''I thought I got a piece of it, but it got up in the air and he batted it out of the air back door. We weren't strong enough. We were too passive there.''
Gaborik also had an assist on L.A.'s first goal of the night.
Quick, who led the Kings to their only Stanley Cup championship two years ago, came up big several times in overtime. Even when he didn't, the Kings held off the Ducks. Quick got out of position during one wild scramble and defenseman Alec Martinez jumped into the net until Quick recovered.
''Unbelievable. It was a little chaotic. Probably owe him dinner there,'' Quick said.
Their rinks just 30 miles apart, the Kings and Ducks have played each other 117 times in the regular season since Anaheim entered the NHL as a Disney-backed expansion franchise in 1993.
They even met at Dodger Stadium in January, with the Ducks winning 3-0. But never in the playoffs, until Saturday night in Orange County.
Game 2 is Monday night at Anaheim.
The Ducks advanced after beating Dallas in overtime in Game 6 of their opening series.
Martinez scored his first goal of the playoffs on a power play 9:04 into the game, beating Hiller on the glove side with a backhander after taking a pass from Gaborik from behind the net. Nick Bonino was in the penalty box for hooking.
Anaheim's Matt Belesky tied it less than three minutes later after a beauty of an assist by Ryan Getzlaf. Getzlaf skated into the Kings zone and behind the net, drawing Quick out of the crease. He passed to Belesky in the slot, who put home a wrister before Quick could get back into position.
It was Belesky's second goal of the playoffs. Getzlaf, who also assisted on Selanne's goal, has nine points in the playoffs.
Hiller, a veteran who came in and saved Game 6 against Dallas - and beat the Kings at Dodger Stadium - got the start over 24-year-old Frederik Andersen.