Harrison (12-4) worked around four walks and struck out three in the victory, during which he allowed only one runner to reach as far as third base.
The Texas left-hander's shutout was his second of the year following a June 8 blanking of San Francisco.
Hisashi Iwakuma (1-2) absorbed the loss for the Mariners, coughing up four runs on seven hits in a five-inning effort.
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