At just twenty years of age, Witt made his major league debut with the California Angels in 1981. Standing 6 feet, 7 inches tall and possessing a great curveball as well as a good fastball, Witt's breakout season came in 1984 when he went 15-11 for the Angels. On July 23 of that year, he struck out sixteen Seattle Mariners during a complete game five-hitter; but the highlight of the year came on the final day of the season, September 30, when he pitched the 11th perfect game in baseball history against the Texas Rangers. He struck out ten and needed just 94 pitches to complete the gem.

From 1984 to 1987, Witt led the Angels every year in wins, strikeouts, innings pitched, and complete games. His best season was 1986, when he was named team Most Valuable Player after compiling 18 wins and a 2.84 earned run average, finishing second only to Roger Clemens for the American League Cy Young Award, and guiding the Angels to within one strike of the World Series.

In the middle of the 1987 season, however, Witt suddenly lost his overpowering stuff and saw his strikeout numbers decline significantly. He did manage to combine with starter Mark Langston to pitch a no-hitter on April 11, 1990 against Seattle, pitching the last two innings; but he was traded to the New York Yankees on May 11, 1990 for Dave Winfield, never winning more than five games during his three years there before retiring in 1993.