Sweet Cat finished third in the 1-mile event, run over turf rated "good" after Thursday's rains.
With John Velazquez riding, Stephanie's Kitten ran just off the early pace, got through along the inside midway down the Churchill Downs stretch and came outside the leader to surge to the lead. She finished in 1:38.80.
Both Stephanie's Kitten and Sweet Cat were sired by Kitten's Joy, the star stallion of Ken and Sarah Ramsey, who has had a significant impact this year on Thoroughbred racing.
Stephanie's Kitten came to the Breeders' Cup off a victory on the all-weather track at Keeneland in the Alcibiades Stakes. She now has three wins and two thirds from five career starts for trainer Wayne Catalano.