Burkett made his debut for the San Francisco Giants late in the 1987 season, and pitched six innings in the majors. He was returned to the minors, where he remained for the next two years. His first full season for the Giants was 1990, during which he went 14–7 with a 3.79 ERA in 204 innings. Burkett's best season came in 1993 when he went 22–7 with a 3.65 ERA for the Giants. Burkett was a National League All-Star in 1993 and 2001. His 1996 postseason complete game win over the eventual World Series Champion New York Yankees was the first complete game in Divisional Series history, and the first postseason win in Texas Rangers history. After being released in Spring Training by the Tampa Bay Devil Rays in 2000, he was picked up by the Atlanta Braves and resurrected a career thought by many to be over. His 3.04 ERA ranked third in all of MLB for 2001. Burkett retired following the 2003 season after going 12–9 with the Red Sox at age 38. He was given the nickname "Sheets" during his days with the Atlanta Braves because of his betting and organizing pools for games in the clubhouse. Although a weak hitter at the plate, batting only.093 with only 18 RBI, Burkett was above average defensively. He recorded a.982 fielding percentage with only 9 errors in 500 total chances in 2,648.1 innings pitched. His career fielding percentage was 26 points higher than the league average at his position.
Professional bowling
Burkett is also a part-time professional bowler, and has 32 perfect games to his credit. He cashed in several PBA Tour events during his baseball days, and joined the PBA50 Tour in 2015. He finished 15th in the 2015 Suncoast PBA Senior US Open and 4th at PBA50 Northern California Classic. His 2016 campaign was cut short when he had right ankle surgery. 2017 PBA50 season top finishes were 11th in PBA50 National Championship, 24th at the Senior US Open, 11th at Dave Small's Championship Lanes Classic, and 9th at the DeHayes Insurance Group Championship. On August 18, 2019, Burkett won a PBA Regional Tour event at the PBA Houston Emerald Bowl Southwest Challenge in Houston, Texas, which was his first PBA title of any kind.
Personal
He has three children named Avery, Maxwell and Reid.