Albarado rode to victory in the 2003 Jockey Club Gold Cup aboard U.S. Horse of the Year, Mineshaft. He has ridden in eight Kentucky Derbys with his best results coming on third-place finishers Steppenwolfer in 2006 and Curlin in 2007. He also rode Steppenwolfer to a fourth-place finish in the Belmont Stakes.
He is the regular jockey for the 3-year-old colt Curlin who was the favorite and finished third in the 2007 Kentucky Derby. Albarado won his first Triple Crown race at the 2007 Preakness Stakes aboard Curlin, edging out Derby-winner Street Sense. Albarado was denied victory at the 2007 Belmont Stakes when Curlin lost to champion filly Rags to Riches by a nose. Albarado also won the 2007 Breeder's Cup Classic aboard Curlin, which was his first Breeder's Cup win.
Robby Albarado was voted the 2004 George Woolf Memorial Jockey Award. That year, on December the 8th, he picked up his 3,000 career win riding Isle of Silver to victory at the Fair Grounds Race Course in New Orleans.