Viola signed with the Minnesota Twins after the team drafted him in the second round of the 1981 Major League Baseball draft. After spending less than a full season in the minor leagues, Viola made his major league debut on June 6, 1982. Although his statistics were fairly disappointing—he finished 11–25 with a 5.37 ERA in the and seasons—Viola became a permanent fixture of the Twins' starting staff for the next 7 seasons, picking up 112 of his 176 career wins.