Jonas Hiller made seven saves in the final 9:58 after rookie goalie Frederik Andersen left with a right leg injury for the Ducks, who bounced back from two narrow losses in Anaheim to open the series.
Ben Lovejoy added a goal with 2:55 to play as Anaheim snapped the Kings' six-game postseason winning streak.
PHOTOS: Playoff action shots
Jeff Carter and Mike Richards scored and Jonathan Quick stopped 19 shots for the Kings, who hadn't lost since Game 3 of their stunning first-round series against San Jose.
Game 4 is Saturday night at Staples Center.
With Quick pulled for an extra attacker, Richards scored with 30 seconds left when he batted home a rebound of Tanner Pearson's shot, but the top-seeded Ducks hung on for just their third win in their last seven playoff games.
Anaheim dropped the first two games of the local rivals' first playoff meeting, scoring just three goals and losing narrow decisions at Honda Center.
Ducks coach Bruce Boudreau curiously changed starting goalies for Game 3, replacing Hiller with Andersen, the Danish rookie who played poorly in all three road games in the first round against Dallas. Boudreau repeatedly said Hiller had played well against the Kings in the first two games, giving up just five goals, but Andersen beat Los Angeles three times in the regular season.
Andersen was solid in Game 3 until getting hurt during a wild scramble midway through the third period. Hiller had to make two tough saves immediately after entering the game, but the Swiss goalie was solid despite Richards' late goal.
The Ducks didn't have the same vociferous road support enjoyed by the Kings at Honda Center earlier in the series, but Anaheim still silenced Staples Center just 4:06 into Game 3.
Ryan Getzlaf got the puck down low to Patrick Maroon, who found Perry in the slot for his third goal of the postseason. Perry, second in the NHL with 43 goals in the regular season, hadn't scored in the series.
The Kings evened it on a power play early in the second period with a play similar to the Ducks' score. Marian Gaborik got the puck low and set up a one-timer for Carter, who hadn't scored a goal in the Kings' last four playoff games.
Anze Kopitar, the NHL's leading scorer with 15 points in the postseason, got the second assist.
Anaheim couldn't score during a 4-on-3 advantage for 59 seconds late in the period, but Nick Bonino found Selanne with a saucer pass for the Finnish Flash's 44th career goal in 126 postseason games. Selanne was a healthy scratch for a game in the first round, but has two goals against the Kings.
Matt Beleskey went to the dressing room early in the third period after a hard hit on the boards by Kings captain Dustin Brown. The Ducks said Beleskey had a lower-body injury.
Lovejoy scored his second goal of the postseason on a 2-on-1 rush with Andrew Cogliano, sending Kings fans to the exits.
