Harrison (2-0) scattered seven hits while throwing 111 pitches. He struck out four and walked two.
No Texas starter has lost a game this season. The only two setbacks suffered by the Rangers have been charged to closer Joe Nathan.
Texas overcame an early 1-0 deficit with a three-run fourth, during which the first four batters reached base.
Anthony Swarzak (0-2) took the loss, allowing four runs on nine hits over seven innings. Minnesota was coming off its first two wins of the season, both against the Los Angeles Angels.
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