Ji-Man Choi, Brandon Lowe and Willy Adames all homered in the fourth inning as the Rays erupted for six runs, wiping out Boston's 4-0 lead.
With one out, Jhoulys Chacín (3.2-4-4-1-5, 57) gave up two singles and a three-run dong to Choi. After a groundout, Lowe blasted a solo shot. Bobby Poyner took over, hitting Kevin Kiermaier and giving up Adames's two-run homer.
Jackie Bradley went 3-for-4. He singled in the second, stole second, and scored on Marco Hernández's double. In the third, Bradley doubled in Mitch Moreland, who had also doubled.
The Red Sox scored twice after two were out in the fourth.