Hawkins was drafted straight out of high school by the Minnesota Twins in the 1991 amateur draft, and spent the next four years in the Twins' minor league system. His major league debut early in the 1995 season was a disastrous start against the Baltimore Orioles, where he gave up seven earned runs in only an inning and two thirds of work. Hawkins bounced between the big league club and Salt Lake of the PCL over the next few years, finally landing in the Twins' bullpen permanently in 1998. He was also the opposing starting pitcher during the perfect game by Yankees pitcher David Wells on May 17, 1998.