Curlin, the top-ranked horse in the world entering the race, got the lead at the top of the stretch in his first try over a synthetic surface. But he could not maintain the advantage, fading to finish fourth behind two Europeans and a local challenger.
Henrythenavigator was second and Tiago was third. The 1 1/4 mile went in track-record time of 1:59.27 over Santa Anita's "Pro-Ride" track.
The outcome puts Horse of the Year honors in doubt with undefeated Breeders' Cup Ladies Classic winner Zenyatta now looking like the favorite for that honor.
Curlin ran his typical race under regular rider Robby Albarado, biding his time in mid-pack until the start of the stretch turn. When Albarado asked him for run, the 4-year-old Smart Strike colt responded and surged past the fading leaders to take the lead.
Raven's Pass, however, was moving right behind Curlin, swung further outside and, under steady urging by jockey Frankie Dettori, got past Curlin to win by 1 3/4 lengths. Henrythenavigator followed, with Tiago just up to edge Curlin by a neck for third.
Gosden said the win over Curlin was special but does not diminish Curlin's glory.
"Curlin set the standard," he said. "Curlin set the benchmark. He's a magnificent horse, and the way he won in the slop last year was superb. In Dubai, he was fantastic. He's a great horse, and he's still a great horse."
Curlin suffered his second defeat of the year. His other loss came in a try on the grass at Belmont Park. In addition to winning last year's Breeders' Cup Classic and earning Horse of the Year honors, he returned this spring to win the Dubai World Cup.
Raven's Pass, a 3-year-old son of Elusive Quality, was bred in Kentucky but has raced in England and France for trainer John Gosden in the name of Her Royal Highness, Princess Haya of Jordan, who leases the horse from Sheikh Mohammed's Darley Stable. He came into the race off a pair of impressive victories in England, the latter a 1-length score over Henrythenavigator in the Queen Elizabeth II Stakes at Ascot last month.
Gosden said before the race he would not have started Raven's Pass in the Classic if it were being run on a dirt track. Santa Anita's synthetic surface, he said, gave European runners who usually race on grass a chance against American dirt specialists.
"For the first time, the top horses from each country can meet for one belt," Gosden said before the race.
Dettori's pre-race comments were prophetic, given the 1-2 finish by the Europeans.
"We always strive to bring our best horses," Dettori said. "I don't think we could have a better bunch than we have now."
Gosden said no decision has been made about racing Raven's Pass next year.
"Those are decisions to be discussed with Princess Haya and Sheikh Mohammed," he said. "And they will be done. So it will be thought about all angles, up and down."