Verlander (2-1) limited the Rangers to one unearned run on four hits, walking three and striking out eight.
Ramon Santiago's two-run single in the fourth put Detroit ahead and the Tigers held on bounce back after a 10-4 loss in the opener.
Nefatli Feliz (1-1) pitched a complete-game loss for Texas, yielding only three hits over eight innings while walking four and striking out six.
Murphy also drove in the Rangers' other run with a sacrifice fly.
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