Beckett (3-4) broke a personal two-game losing streak, scattering four hits and striking out nine while yielding a pair of walks.
The Red Sox ace threw 60 of his 93 pitches for strikes while rebounding from a disastrous Thursday outing in which he lasted only 2 1/3 innings against Cleveland.
Rich Hill and Alfredo Aceves finished up with one hitless frame each for Boston, which notched its fifth straight win.
Seattle's Blake Beavan (1-4) turned in his fifth consecutive start without a win, giving up three runs on five hits in a four-inning effort.
The Mariners sustained their fifth loss in seven games.