Baker was called up on May 2, 2005; "Baseball Prospectus" speculated he might make starts in place of Kyle Lohse; Twins' manager Ron Gardenhire said he might be used to start if Lohse did not continue to improve. Baker did not wind up starting, making his MLB debut by pitching one scoreless inning out of the bullpen in an 8–1 victory over the Tampa Bay Devil Rays on May 7. That was his only appearance with the Twins in May. He was recalled in July to make his first major league start. On July 5, he pitched five innings, giving up just two runs on five hits and striking out five; however, he took the loss in a 2–1 defeat to the Los Angeles Angels of Anaheim. Though he was expected to get sent back to Rochester, Twins' manager Ron Gardenhire had praise for him, saying after the game, "We think we have a quality major leaguer