Ross homered after Eric Chavez drove in Paul Goldschmidt earlier in the inning to tie the game 1-1.
Ross's homer came off Jeremy Hellickson (10-5), who was hung with the loss after coughing up five runs in 4 2/3 innings.
Wade Miley (9-8) picked up the win for Arizona. The Diamondbacks won for the fourth time in nine tries as they struggle to keep pace with the meteoric Los Angeles Dodgers in the NL West.
Evan Longoria had a solo home run for the Rays.
Celebrity Families of 2014 [PHOTOS]