Over the next two seasons, Hawkins served as a setup man for Guardado. In 2002, Hawkins was used mainly in the seventh and eighth innings. He appeared in 65 games, winning all six of his decisions, posting a 2.13 ERA, and striking out 63 hitters in innings pitched. The Twins won the AL Central Division title, and Hawkins made three appearances in the AL Division Series (ALDS) against the Oakland Athletics, striking out five batters in scoreless innings as the Twins defeated Oakland in five games. He appeared in four games in the AL Championship Series (ALCS) against the Anaheim Angels as well, but his ERA was 20.25 this time, and the Angels defeated the Twins in four games. The next season, he was primarily used in the eighth inning. He posted a 9–3 record and struck out 75 hitters in innings. His 1.86 ERA was fifth-lowest among AL pitchers who threw at least 60 innings, and his 74 appearances were fifth-highest among AL pitchers. For the second year in a row, the Twins won the AL Central Division title, this time facing the New York Yankees in the ALDS. In Game 1, Hawkins was awarded the win after pitching a scoreless seventh and eighth innings. However, he would post a 6.00 ERA in three appearances in the series, which the Yankees won three games to one. Hawkins became a free agent after the 2003 season.