Buchholz (10-0) made his first start in more than three months following a shoulder injury but showed few signs of rust, scattering three hits in the 74-pitch performance.
The right-hander issued one walk and struck out six for the American League East-leading Red Sox, who reeled off a ninth win in 11 games.
Tampa Bay's David Price (8-8) was saddled with the loss, allowing two runs on just three hits over eight innings. He didn't issue a walk and struck out nine.
Despite the defeat, the Rays' lead for the second and final AL wild card spot remained at 1 1/2 games over Cleveland and Baltimore, each of whom also fell Tuesday.
Their advantage over New York, however, dwindled to two games after the Yankees' Tuesday win over the Orioles.
2014: The Year in Music [PHOTOS]