Odorizzi (7-8) gave up one run on three hits while striking out five for the Rays, who are 10-1 since July 12. The right-hander has won three straight starts and is 5-1 in his past six decisions.
James Loney hit a two-run single in the sixth for Tampa Bay.
Mark Reynolds hit a solo homer for the Brewers, who saw starter Kyle Lohse (11-5) give up two runs on four hits over six innings. Lohse, who had won back-to-back starts, struck out six and walked three.
Notable deaths of 2014 [PHOTOS]
Arizona Cardinals player formally charged