Giguere, the NHL leader with 23 wins, made 14 saves for Anaheim before leaving late in the second period. He was hurt when his skate apparently got caught near one post as Sharks rookie Joe Pavelski skated behind his net, allowing Steve Bernier to score the tying goal.
Michael Wall relieved Giguere and had to make just four saves in his second NHL appearance. The Sharks' offence faltered when Giguere left, and Perry broke a tie by deflecting Samuel Pahlsson's long shot past Evgeni Nabokov, who made 26 saves.
Chris Kunitz and Dustin Penner scored for the NHL-leading Ducks, who still haven't lost consecutive games in regulation during one of the greatest starts in league history. Anaheim has a franchise-record 62 points in its first 39 games.
Anaheim's Travis Green scored from the blue line on the first shift of his first game in a month to open the third chapter of the burgeoning rivalry between the Pacific Division's top teams. They split the first two meetings this season, with San Jose beating Anaheim 4-3 just 10 days earlier.
Christian Ehrhoff and Patrick Marleau also scored for the Sharks, who have lost three of five on a six-game homestand. San Jose got a late two-man advantage, but couldn't score on a lengthy power play.