The Ducks, holding the No. 2 seed in the Western Conference, won their second straight after dropping 13 of their previous 19.
The Kings, last in the conference, have lost 13 of 17, including two in a row.
The teams meet again Sunday in Anaheim.
Perry beat a sprawled Garon in the fifth round of the shootout after Alexander Frolov led off for the Kings with a miss.
In the second round, Michael Cammalleri went top-shelf against Jean-Sebastien Giguere, who made 30 saves in regulation for his 28th victory. Teemu Selanne answered for the Ducks with a last-second move that lifted the puck to the top of the net.
Kings rookie Anze Kopitar tied the game at 2-2 with barely five minutes left in regulation and leaped Spiderman-like on the glass in celebration. He and Lubomir Visnovsky, who got the assist, have six points each in five games against the Ducks this season.
The Ducks snapped a 1-1 tie on Chris Kunitz's goal at 5:48 of the third. He jammed the puck in after Andy McDonald worked it around the back of the net. McDonald and Selanne, the NHL's top point producing team with 239, assisted on Kunitz's career-high-tying 19th goal.
Selanne tied the score on his NHL-leading 19th power-play goal at 3:22 of the second. Chris Pronger's one-timer deflected off the stick of Dustin Penner, standing in the slot, and went toward Selanne, who was waiting off to the left. Selanne's shot hit the right post and went in for his 300th career goal with Anaheim, tying Paul Kariya's franchise record.
Frolov gave the Kings a 1-0 lead on a power-play goal with eight seconds remaining in the first. Brent Sopel's pass from along the boards hit Frolov's stick and the puck sailed in for his team-leading 31st goal.
Garon stopped 31 shots for the Kings, who were limited to three shots in the third when Anaheim had 11.
The first period was dominated by 56 minutes of penalties, including three misconducts. Two of those went to Aaron Miller and Raitis Ivanans of the Kings; the other went to Anaheim's Samuel Pahlsson, who, like Miller, was involved in a major fight that resulted in penalties to Pronger and Derek Armstrong.
Notes: Kings D Mattias Norstrom sustained a lower body injury in the first period and didn't return. ... The Ducks lead the season series 4-1. ... The announced attendance of 18,118 was the Kings' seventh sellout. ... The Kings signed RW John Zeiler to a one-year contract Saturday and recalled him from the AHL's Manchester Monarchs. Zeiler was in uniform for the game. F Konstantin Pushkarev was assigned to Manchester.