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.
Celebrity Couples of 2014 [PHOTOS]