The White Sox scored three times in the eighth, helped by a Mariners misplay.
Paul Konerko led off with a fly and the ball glanced off center fielder Michael Saunders' glove and then hit him for a two-base error.
With two outs and runners at the corners, Ramirez hit a slow grounder to shortstop Brendan Ryan and beat the throw as pinch-runner Brent Lillibridge scored. Alejandro De Aza added a two-run single.
Addison Reed pitched the ninth for his seventh save in as many chances.
Jesse Crain (1-0) got the win. Shawn Kelly (0-2) took the loss.
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