Jones could not continue his success into the 2001 season. After blowing 6 of his first 17 save opportunities, Jones lost his closer role and the Tigers traded him to the Minnesota Twins on July 28, 2001. After the 2001 season, Jones became a free agent and signed with the Colorado Rockies. While playing for the Rockies in April , Jones made remarks criticized as anti-gay comments during a discussion of the play "Take Me Out". Jones publicly apologized, but did not retract his comments. He made his first career postseason appearance that year, pitching to three batters in Game 6 of the ALCS as the third Red Sox pitcher against the New York Yankees. In the sixth inning, he allowed a hit while garnering a strikeout and a walk before being taken out for Alan Embree. The Red Sox won the game 9-6 with six pitchers used, but they lost the ALCS the next night. Jones left the Red Sox after the season.