Devers' 11th homer of the season capped a five-run, two-out rally in the third against Seattle starter Mike Leake (7-4).
Andrew Benintendi and Bogaerts began Boston's rally with a pair of singles. J.D. Martinez drew a nine-pitch walk to load the bases before Mitch Moreland drove in two with a single to centerfield, and Devers followed with a blast off the Hit It Here Cafe in right field to give Boston a 5-0 lead.
The Red Sox pulled away in the seventh against right-handed reliever Chasen Bradford, who gave up three runs and two homers while getting two outs.
Bradley Jr. sent Bradford's first pitch over the center field wall for his fourth home run this season. Benintendi hit his third single of the game with one out before Bogaerts put Boston ahead 8-2 with a shot into the bullpen in left centerfield, his 12th of the season.
Facing left-hander Roenis Elias in the eighth, Benintendi extended Boston's lead to 9-2 with a sacrifice fly to center.
Boston starter Eduardo Rodriguez picked up his sixth victory in a row, allowing two runs on six hits while striking out nine. Rodriguez (9-1) has allowed two or fewer runs in each of his starts during his winning streak.
The Mariners loaded the bases with no outs for the heart of their order against Rodriguez in the fifth, but managed just one run. Jean Segura cut Seattle's deficit to 5-2 with a fielder's choice, but Seattle's rally was cut short following back-to-back fly outs from Mitch Haniger and Nelson Cruz.
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Cruz hit his 17th home run of the season in the fourth, sending a 3-2 fastball from Martinez 442 feet into the upper deck in left field to trim Seattle's deficit to 5-1. In the eighth, Ryon Healy doubled down the left field line, scoring Cruz to make it 9-3.
Red Sox: Chris Sale (6-4, 2.75 ERA) takes the mound as the Red Sox continue their road trip against the Twins on Tuesday. Sale has allowed just one run in each of his last two starts and has nine starts this season allowing one or fewer earned runs.
© 2018 by Associated Press.