Baker grew up in Shreveport, Louisiana, and attended Oklahoma State University. He was drafted by the Twins in the second round of the 2003 amateur entry draft and reached the major leagues in 2005. In 2006, he made their starting rotation out of Spring training but struggled and was sent to the minor leagues for most of the rest of the season. Beginning 2007 in the minors, he was called up in May and nearly threw a perfect game on August 31. He went 11–4 in 2008 and posted a 3.45 earned run average (ERA). In 2009, Baker logged a career-high 200 innings and started the American League (AL) tiebreaker game against the Detroit Tigers which the Twins won to advance to the postseason. He had a 12–9 record in 2010 but battled injuries towards the end of the year and was left out of the Twins' postseason rotation. Injuries limited Baker in 2011 again, but he was the only Twins' pitcher to post a winning record. He missed 2012 after undergoing Tommy John surgery; this also caused him to miss most of 2013, which he spent with the Chicago Cubs. He began 2014 in the minor leagues but was later added to the Texas Rangers' roster. Baker started eight games for the Rangers but was used mainly as a relief pitcher. In 2015, he signed with the New York Yankees but was released before the season started. Signed by the Los Angeles Dodgers, he started two games for them, the last appearances of his major league career.