Nathan was traded to the Minnesota Twins on November 16, 2003. The Giants sent Nathan to the Twins along with pitchers Boof Bonser and Francisco Liriano for catcher A. J. Pierzynski and cash. The Twins decided to make Nathan their closer starting in 2004, risky move considering that Nathan had notched only one save in six opportunities as a Giant, but he won the job over J. C. Romero and Jesse Crain in spring training. He was signed to a three-year deal on March 4, 2004 and agreed to an incentive-laden contract with a base salary of $440,000. He started off the season strong, allowing no runs in 20 appearances and earning 14 saves from April 15 to June 4. He was named AL Co-Player of the Week starting on May 10 with four saves in four innings and four appearances, facing the minimum number of batters each time. His credentials for the first half of the season, 23 saves in 24 opportunities with a 1.19 ERA in 26 appearances, earned him his first All-Star appearance in the 2004 MLB All-Star Game. He was the only Twin on the squad and pitched a perfect seventh inning, getting Bobby Abreu to strike out, Mike Lowell to fly out and Miguel Cabrera to strike out. His numbers were impressive through the rest of the season, allowing no runs between June 9 and August 18, and between August 25 and September 16. and finishing 2004 with 44 saves in 47 opportunities and an ERA of 1.62. The Twins won the AL Central division and faced the New York Yankees in the ALDS. Nathan picked up his first postseason save in Game 1, but blew his second opportunity in Game 2 as the Twins went on to lose the ensuing three games. His outstanding season earned him MVP and Cy Young votes, finishing fourth for Cy Young and 12th for MVP. His first child, a son named Cole, was born on November 9, 2004.