Pajon, the flagbearer for her country during the opening ceremony, led from the start on the challenging course. Sarah Walker of New Zealand claimed silver, and Laura Smulders of the Netherlands took bronze.
Crain had moved up to the U.S. Olympic Team after teammate Arielle Martin suffered serious injuries in a bike crash last week during a training session. She has been riding in the Olympic games with the initials of her injured teammate on the palm of her left glove.
During the seeding round on Wednesday, Brooke crashed on the last lap of the race. She had the wind knocked out of her and suffered a bruised thigh. She was able to recover for Friday's semifinal race.
In Friday's semifinal race, one of the gold medal favorites Squel Stein of Brazil crashed and was taken from the course on a stretcher. Stein fell off her bike after she landed on the grass following a big jump in the first half of the course. The 21-year-old Stein secured her best result in a major competition earlier this year when she reached the world championships final.
The Associated Press contributed to this report