Playing for the Colorado Rockies from the season until , Norton compiled a .252 batting average in 344 games played. Norton played four positions for the Rockies his first year with the team, including starting at first base for All-Star Todd Helton for the only 5 games Helton rested that year. In his final year with the Rockies, Norton led the majors in successful pinch hits and pinch-hit RBI. However, Norton was granted free agency at the end of the 2003 season. was a forgetful year for Norton, as he split time with the Detroit Tigers and their minor-league team, Toledo. Tigers first baseman Carlos Pena led the team in home runs that year, leaving very little room for Norton. A knee inflammation also kept him on the disabled list for over a month. On January 11, , he signed a minor league contract with the Tampa Bay Devil Rays. He was brought up to the majors on April 26 when Jorge Cantu was placed on the disabled list. In Norton's first year as a D-Ray, he bested his season home run total (17) and started a career high 26 games in right field. He missed making the Opening Day roster while going under the knife to surgically repair his right knee. On Mother's Day, May 14, 2006, Norton was one of more than 50 hitters who brandished a pink bat to benefit the Breast Cancer Foundation
On February 13, , Norton signed a minor league contract with an invite to spring training with the Seattle Mariners. He was purchased from the minors and added to the active roster on April 11, when Charlton Jimerson was designated for assignment. On April 30, Norton was designated for assignment despite batting .438 in 16 at-bats. On May 5, Norton was traded to the Atlanta Braves for cash considerations.