Adrian Beltre and Mitch Moreland each provided a two-run blast and Leonys Martin added a solo shot for Texas, which outscored the Mariners 23-3 in the three-game series.
Justin Grimm (1-0) claimed the victory in his fourth major league start, holding Seattle to two runs (one earned) on six hits over six innings. The right-hander struck out nine while issuing only one walk.
Michael Kirkman collected his first career save with three innings of one-run relief.
M's starter Aaron Harang (0-2) was lit up for eight runs on eight hits over 4 2/3 innings.
Kyle Seager went 3-for-4 with a homer and two RBI as Seattle fell for the fifth time in six contests.