Murphy delivered a two-run double in the second inning, handing Texas a 3-0 lead, and capped the scoring with an RBI single in the sixth.
In between, Nelson Cruz connected for a solo shot as the Rangers improved to an MLB-best 32-17 with a third straight victory.
Holland (4-2) was touched for two unearned runs on four hits, striking out 10 while walking three in logging his fifth straight start without a loss.
Robbie Ross and Tyler Scheppers combined for 1 1/3 scoreless relief frames, and Joe Nathan tossed a 1-2-3 ninth for his 16th save for Texas.
Mariners starter Felix Hernandez (5-4) surrendered five runs on 11 hits over 5 2/3 innings.
Kendrys Morales drove in both Seattle runs.