Peavy became the third pitcher in White Sox history to win the award, joining Jim Kaat (1974 and '75) and Mark Buehrle (2009, '10 and '11). Earlier Tuesday, Peavy agreed to a two-year, $29 million contract extension.
Peavy committed one error in 37 chances in 2012, and opponents were successful on just 52.9 percent (9-of-17) of their stolen-base attempts when the right-hander was on the mound.
The White Sox have had a Gold Glove Award winner the past four seasons, just the third time in franchise history that feat has been accomplished. The organization also had at least four straight years with a Gold Glove winner from 1990 to '93 and 1957 to '63.