Jason Varitek snapped an 0-for-14 slide with his tiebreaking, sixth-inning solo homer off James Shields. Kevin Youkilis also homered off the Rays starter.
Red Sox ace Josh Beckett, who struggled in his first two starts of the playoffs, allowing two runs and four hits in five innings, and Hideki Okajima, Justin Masterson and Jonathan Papelbon combined for hitless relief.
B.J. Upton tied an AL record with his seventh home run of the postseason, and Tampa Bay tied it 2-2 on Jason Bartlett's fifth-inning homer. But the Rays didn't get another hit, and Boston improved to 9-0 in ALCS elimination games under manager Terry Francona.
Now Jon Lester starts Game 7 for the Red Sox on Sunday night against Matt Garza in a rematch of Game 3, won by the Rays 9-1 at Fenway Park.