Millwood (5-12), making his 27th start of a struggling season, limited the Red Sox to four hits with three strikeouts and left the game with Seattle clinging to a one-run lead.
Stephen Pryor, Charlie Furbush, Josh Kinney, Lucas Luetge and Tom Wilhelmsen then teamed to shut down Boston.
Wilhelmsen walked the leadoff man in the ninth, then retired the next three batters for his 24th save.
Dustin Ackley drove in both Seattle runs with a first-inning single off Aaron Cook (3-9).
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys