The team also declined its $6 million option on designated hitter Luke Scott, instead paying him a $1 million buyout.
Shields, who was 15-10 with a 3.52 ERA last season, gets a $9.5 million salary next year rather than a $1.5 million buyout. The 30-year-old right-hander ranked third in the American League in innings (227 2-3), fourth in strikeouts (223) and 12th in ERA. He has pitched 200 or more innings in six consecutive seasons.
Tampa Bay has a $12 million option on Shields for 2014 with a $1 million buyout
Rodney, the AL comeback player of the year, set a club record with a career-best 48 saves in his first season with the Rays. The 35-year-old right-hander had a 0.60 ERA, a big league record for a reliever with at least 50 innings pitched. Tampa Bay picked up his $2.5 million option rather than pay him a $250,000 buyout.
Molina, 37, gets $1.5 million next season instead of a $300,000 buyout. He batted .223 and set career highs with eight homers and 32 RBI in 102 games this year, his 13th in the majors.
The 34-year-old Scott hit .229 with 14 home runs and 55 RBI in 96 games during his first year with the Rays. He was on the disabled list twice and missed 45 games.