Evan Longoria and Carlos Pena had solo home runs for the Rays, who took a 2-1 lead in the best-of-seven series with the four-homer attack. The Tampa Bay bats has hit seven homers in the last two playoff games.
Matt Garza (1-1) earned the win by scattering six hits and allowing only one run in six-plus innings.
Jacoby Ellsbury drove in the lone run for the Red Sox. Dustin Pedroia and Mark Kotsay each had two hits in defeat.
Jon Lester (1-1) gave up five runs on eight hits - over 5 2/3 innings. The left-hander struck out seven and walked two.
Game 4 is scheduled for Tuesday night in Boston.