From the town of Aguas Benditas-Chilibre, Panama, Corpas was signed by the Colorado Rockies at the age of 16 as an amateur free agent in 1999. He made his debut for the Rockies on July 18, 2006. Following the All-Star Break in 2007, Corpas filled in as closer for Brian Fuentes, who was demoted after taking four of eight losses during an 8-game losing skid. Corpas finished the year with a 4–2 win-loss record, a 2.08 earned run average, and 19 saves in 22 chances; he continued to serve as the Rockies' closer during the 2007 postseason.
He continued as the closer into the 2008 season. However, after a number of poor outings, he was replaced by Fuentes in late April. In 2008 he tied for the major league lead in blown saves, with 9.
During 2009 spring training, he competed with Huston Street for the closer spot; Street won the position and Corpas started the season as the eighth inning set up pitcher. After poor performances by Street, Corpas was renamed the closer on April 17; however, Corpas also pitched poorly, and the closer job was given back to Street on May 1.
On January 9, 2013, Corpas signed a minor league contract with the Rockies. His contract was purchased from Colorado Springs (PCL) on June 2, 2013. He was outrighted off the roster and elected free agency October 17, 2013. Corpas rejoined the Rockies for the 2014 season, agreeing to a minor league contract. On July 13, 2014, Corpas was released by the Rockies.