The Red Sox (4-9) are off to their worst start since opening 1996 at 2-11. Boston finished 0 for 30 with runners in scoring position during the series, with Jeremy Hermida's two-run homer the only run in the finale.
Jeff Niemann (1-0) pitched seven sharp innings to help Tampa Bay win its seventh straight, all on the road, and match the club's best winning streak away from Tropicana Field in one season. The Rays last won seven in a row in June 2004.
It was also Tampa Bay's first sweep of a series three games or more in Fenway Park.
Niemann gave up two runs, five hits, walked three and fanned two. He held the Red Sox to three hits until Bill Hall singled off the wall and Hermida followed with his homer into the right-field seats with two outs in the seventh.
John Lackey (1-1), who signed a 5-year, $82.5-millon contract during the offseason, allowed eight runs and nine hits in only 3 1/3 innings. He didn't get much help from the Boston defense, either, with all three outfielders — Hermida, Hall and J.D. Drew — misplaying a ball into an extra base or making an error early in the game.
There were loud boos when Hall watched a ball carom off the center-field wall and away from him, allowing Jason Bartlett to take third. The play was originally ruled a double and an error, but changed later to a triple.
The boos didn't stop when Drew grounded out to end the game.
Carl Crawford was successful stealing for the 31st straight time against the Red Sox, swiping second in the third inning.
Bartlett opened the game with a double, snapping an 0-for-14 stretch, advanced on Crawford's sacrifice and scored on Ben Zobrist's grounder.
Evan Longoria had a two-run double in the third and Upton belted his homer into the Red Sox bullpen, just past the outstretched glove of Hall, to make it 6-0. It was Upton's fourth homer in five games.
Barlett added an RBI triple, chasing Lackey and making it 7-0 in the fourth. He scored on Crawford's sacrifice fly.
Notes
The Rays have won eight straight road games dating to last season. … Red Sox CF Mike Cameron was a late scratch. Manager Terry Francona said he had similar symptoms to last week, when he missed two games with a kidney stone. … Drew is 2-for-24, and Kevin Youkilis is in a 1-for-19 slump. … Meghan Duggan of the Olympic silver medalist U.S. hockey team threw out the ceremonial first pitch. The first official pitch was 11:07 a.m.