Before turning to riding, Espinoza drove a bus in his hometown of Mexico City. He took riding lessons on a farm outside of Mexico after high school, and then attended jockey school for a year, which is a requirement in Mexico.
Four months after winning his first race at Hippodromo de las Americas he moved his tack to the U.S. His brother Jose rides in New York and another brother, Leo, is a former jockey. Espinoza rode at Santa Anita and then moved to Northern California, where he was the leading apprentice at Bay Meadows and Golden Gate Fields. He headed back down the coast to the more lucrative Southern California circuit and won riding titles at Fairplex in 1996 and 1997. Espinoza had a breakout year in 2000 when he won or shared three major riding titles, won 15 graded stakes and finished seventh nationally with $13.2 million in purse earnings.
In 2002, he won the Kentucky Derby and the Preakness on War Emblem. The colt, trained by Bob Baffert, went to his knees leaving the gate of the Belmont Stakes and subsequently finished eighth. Espinoza's top mounts include The Tin Man, Evening Jewel, The Usual Q.T., Spain and Smiling Tiger.
Espinoza is the regular rider of likely 2014 Kentucky Derby favorite California Chrome.