The 28-year-old left-hander, making his third start and his first at home since returning from back surgery rehab, came up with a solid -- if not deep-- effort of 5 1/3 innings of shutout work.
Harrison limited the Rockies to three hits and the Rangers snapped a three-game losing streak.
The key for Harrison was escaping a jam in the second inning thanks to a double play after the Rockies loaded the bases with one out. Control was a stumbling block with four walks driving up his pitch count to 97.
Some quick thoughts:
Rocket arm: Alex Rios took a run away from the Rockies with a one-hop throw to the plate from medium-deep right field in the seventh inning. Catcher Robinson Chirinos applied the tag on Michael McKenry, trying to score from third after tagging. Rockies skipper Walt Weiss lost a challenge of the call after a two-minute, 30-second delay.
Hammer time: Prince Fielder launched a Franklin Morales pitch 401 feet into and out of the upper deck of the home-run porch in the sixth inning to extend the Texas lead to 3-0. He tied Shin-Soo Choo for the club lead with three. All three of Fielder's homers have come with the bases empty.
Keep 'em coming: When Rougned Odor started at second base, he became the 36th player to be used by the club this season. Coming into Thursday, the New York Yankees and Los Angeles Angels are the only teams in the majors to use 36 players this season.
Glove work: The first ball hit to Odor as a major leaguer resulted in a double play. Odor moved left to glove McKenry's ground ball and snapped a perfect throw to Elvis Andrus covering second base to start the twin killing that ended a bases-loaded Rockies threat in the second inning. Odor and Andrus narrowly missed combining on another double play in the fifth. Odor got rid of the ball quickly for the out at second, but Charlie Blackmon's speed beat Andrus' throw to first.
Home cooking: Leonys Martin extended his home hitting streak to 10 games with an RBI single to right field for the game's first run in the second inning. Martin came into the game batting .382 in 17 home games, third best in the AL.
Stealing a run: The Rangers' offense has been station-to-station the last few days facing big deficits. But with a 1-0 lead, Martin made a daring break for third in the second inning. Andrus struck out on the pitch for the second out but McKenry's errant throw allowed Martin to trot home with the second run. Martin reached second on a balk.
Tack-on runs: Michael Choice's RBI single in a two-run seventh gave the Rangers breathing room.
Relief on the way: Nick Martinez struck out Jordan Pacheco with two in scoring position in the sixth when the Rangers lead was only 2-0. Aaron Poreda, Jason Frasor and Joakim Soria completed the shutout.
Check the board: When the Rockies didn't score in the first inning, it ended a streak of 26 consecutive innings in which the Rangers had trailed.