In 2007, Burnett was selected to Midwest League All-Star Game while playing with the Twins' low A affiliate, the Beloit Snappers. He ended the season with a 3.02 earned run average, which was fifth best in the league. Burnett compiled a 5 – 2 record with a 3.36 ERA over 14 appearances in the first half of the 2008 season—helping his team capture the Florida State League first-half West Division title. Scout.com called him one of the best right-handed pitchers in the Twins' organization. On August 21, 2008, in only six innings, Burnett struck out a career best ten Lakeland Flying Tigers in the Miracle's 8-1 win at Joker Marchant Stadium in Lakeland. Burnett, Carlos Gutiérrez and Anthony Slama combined on a new season-high 17 strikeouts on the night. His best pitching performance of the season, however, may have been his last. With the Miracle already leading their first round play off series against the Dunedin Blue Jays 1-0, Burnett pitched six innings of shutout ball, giving up only two hits against the second half division winners. The Miracle went on to win the game 3-1 to advance to the second round of the play offs for the first time since 1995.
He was converted to a reliever in 2009, and combined to go 3-3 with a 1.85 ERA, thirteen saves and 78 strikeouts in 78 innings for the Fort Myers Miracle and the Twins' Double-A affiliate, the New Britain Rock Cats. He made the Twins out of Spring training 2010 without having ever played at the triple-A level. Burnett made his major league debut on April 8, 2010, retiring all three batters he faced in a 10-1 win over the Los Angeles Angels of Anaheim. On April 15, 2010, the Twins sent Burnett to their triple-A affiliate, the Rochester Red Wings. Twins manager Ron Gardenhire said the move was partly so Burnett could get more regular playing time. He was recalled to the Twins just two days later, when they placed reliever José Mijares on the disabled list. Burnett continued to pitch regularly for the Twins, and remained on the roster when Mijares was reactivated. Burnett earned his first major league win on June 5, 2010, over the Oakland A's. On July 19, the Twins optioned Burnett to Rochester and recalled pitcher Anthony Slama. He remained in Rochester until he was recalled on September 3, earning a win in his first appearance back in the majors.
On March 29, 2013, Burnett was claimed by the Toronto Blue Jays, and optioned to their new Triple-A affiliate Buffalo Bisons. On April 10, Burnett was designated for assignment by the Blue Jays to make room for waiver claim Casper Wells. He was claimed off waivers by the Baltimore Orioles on April 12, and sent to the Triple-A Norfolk Tides. He was called up by the Orioles on April 22, and sent back to Norfolk on April 24. Burnett was called up again on May 9 when Miguel González was placed on the 15-day disabled list. He was optioned back to Norfolk on May 11, and recalled again on May 14 when Wei-Yin Chen was placed on the disabled list. He was optioned back to Norfolk again on May 18, but was designated for assignment on May 23 to make room on the roster for Kevin Gausman.
The Chicago Cubs claimed Burnett on waivers on May 27, 2013. The Cubs optioned him to the Triple-A Iowa Cubs on May 30. He was designated for assignment on June 1, 2013, and sent back to the Iowa Cubs on June 3. He elected free agency on November 14, 2013.
