Vargas (10-7) won his third straight start, limiting Tampa Bay to a run scored on Ichiro Suzuki's fielding error in the seventh inning.
The left-hander allowed seven hits and three walks, and struck out five for the Mariners, who evened their three-game set at Tropicana Field.
Shawn Kelley, Oliver Perez and Brandon League combined for two scoreless relief frames and Tom Wilhelmsen racked up his ninth save.
Seattle scored both of its runs on Michael Saunders' first-inning single.
Tampa Bay starter Alex Cobb (4-7) surrendered two runs on three hits before leaving the game after two innings. He was helped off the field after being hit in the shin with a ball off the bat of Suzuki.
The Rays hurler was later diagnosed with a leg contusion.
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