With the score tied 2-2 and the bases loaded in the fifth inning, Morrison hit a ground ball past first base against Texas starter Wandy Rodriguez (0-1). Morrison finished 4 for 5, including two hits against Rodriguez to improve to 7 for 14 in his career against the left-hander.
Hernandez allowed five hits, two runs and one walk in 6 2-3 innings to improve to 4-0 for the first time since 2009.
Fernando Rodney pitched a perfect ninth inning for his seventh save in eight opportunities. He saved all three games as the Mariners swept the series for their first three-game winning streak this season.
Seattle's Nelson Cruz was 2 for 4, including his 10th home run to lead off the second inning.