Aaron Hill, playing his first game for the Red Sox, ripped a pair of RBI singles to contribute to the cause. David Ortiz unloaded for his 21st homer, a towering shot to right in the fourth.
Chris Archer (4-12, 4.66 ERA) took the loss for the Rays, allowing seven hits and five runs over six innings.
Red Sox right-hander Sean O'Sullivan labored in the fifth, and the Rays came back with two runs, getting a game-tying, RBI single by Evan Longoria.