The homer, Thome's 30th this season, was the 537th of his career, one better than Mickey Mantle, to give him sole possession of 14th place on the all-time list.
One of Nick Swisher's two hits was a seventh-inning two-run homer. Paul Konerko's only hit was a solo blast in the sixth.
A.J. Pierzynski had three hits, and a total of three players had two hits for the White Sox, who have won three in a row.
The winning pitcher, after retiring the only batter he faced, was Ehren Wassermann (1-1).
LA's Juan Rivera hit a two-run sixth-inning homer. Four others had one RBI and three players had two hits for the AL West-leading Angels, who have lost three of four overall.
The losing pitcher was Justin Speier (1-8).
Closer Francisco Rodriguez blew his sixth save.