Bradley's homer in the fifth broke a 7-7 tie. Boston added three more runs in the eighth to hold the Mariners at bay.
Craig Breslow (3-2) picked up the win as one of five Boston relievers who took over after starter Allen Webster exited after 2 1/3 innings.
Ortiz went 4-for-5 and increased his career hit total as a designated hitter to 1,688. He tied Harold Baines for the most hits by a DH in Major League history.
Blake Bevan (0-2) was hung with the loss for Seattle. Brad Miller drove in four runs for the Mariners had won five of their previous seven games.