Vargas (14-9) broke a personal three-start losing streak, baffling the Red Sox on six hits while striking out five. The left-hander didn't issue a walk, tossing 71 of his 102 pitches for strikes.
Josh Kinney turned in a scoreless eighth inning and Tom Wilhelmsen notched his 23rd save with a 1-2-3 ninth as the Mariners took the opener of a three-game series and won for the 13th time in 19 contests.
Boston's Clay Buchholz (11-5) was saddled with the defeat, allowing four runs (three earned) on six hits over seven complete innings.
Cody Ross drove in the only run for the reeling Red Sox, who dropped their seventh straight.