Hunter (1-1) made his sixth start in the majors and gave up a run on three hits with five strikeouts over 5 1/3 innings.
Three Texas relievers tossed 3 2/3 hitless innings, with Frank Francisco claiming his ninth save.
Hunter has moved into the rotation to replace Matt Harrison, who was put on the disabled list last week with biceps inflammation.
The Rangers, who had just five hits, won their third straight after losing three in a row.
Blalock put Texas in front with his homer in the fourth off Scott Kazmir (4-5). Marlon Byrd doubled home the other Texas run in the fifth.
Copyright 2009 by United Press International.
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