The 27-year-old Fields was a combined 4-3 with 12 saves and a 2.01 ERA for Triple-A Pawtucket and Double-A Portland. The right-hander struck out 78 and walked 18 in 58 1-3 innings.
There were 15 players picked in the major league portion of the Rule 5 draft. Teams pay $50,000 to select them and must keep them on the big league roster throughout 2013 or offer them back to the original club for $25,000.
Steven Hill, who played nine games for St. Louis last season, was taken by Oakland in the Triple-A phase. He made his major league debut in 2010, homering in his only game that year for the Cardinals. Hill played first base, third base, the outfield and catcher in Triple-A last season.