Right fielder Shin-Soo Choo hit for the cycle with a triple to open the ninth and drove in three runs to support Harrison.
"I'm not thinking about it because it's not an easy pitcher on the mound," the left-handed hitting Choo said of left-hander Rex Brothers. "I tried to hit the ball hard. I hit it well...I'm not thinking about it before contact."
The victory was Harrison's first in the big leagues since May 8, 2014, when he beat the Rockies in Texas. Six days later, Harrison went on the disabled list with a back condition that led to season-ending spinal fusion surgery.
He won 14 games for the Rangers in 2011 and 18 the following year. But since the beginning of 2013, Harrison has undergone four surgeries, three on his back.
"Huge confidence booster," said Harrison, who got 11 outs on ground balls in his Coors Field debut. "Today I felt the best I felt in a couple of years. There was an adjustment we made in the bullpen to get me to go more downhill. My sinker was sinking a lot more today. I was able to move the ball easier in and out."
Harrison worked four innings in his 2015 debut for the Rangers on July 8, allowing six runs in a loss against Arizona. But Harrison (1-1) stifled the Rockies, allowing six singles and one double and getting double plays to end two innings.
"It looked like his two-seamer had some depth to it," Rockies manager Walt Weiss said. "He was making us hit the top of the ball. He had a good fastball-changeup mix. He spotted the fastball, took shots in with it and had a real good changeup. That was his go-to (pitch).
Center fielder Delino DeShields had a career-high four hits and two RBIs, finishing a home run shy of the cycle. First baseman Prince Fielder hit his 15th homer and had two hits for his major league leading 40th multiple-hit game.
Rockies starter Kyle Kendrick (3-11) allowed a season-high tying 10 hits and six runs in 4 1/3 innings. He yielded Choo's 12th homer, the major league leading 24th homer Kendrick has allowed this season. Kendrick's 11 losses are tied for the most in the majors, and the Rockies are 5-14 games he has started.
Kendrick, whose ERA is 6.12, was unavailable for comment after the game. Weiss said Kendrick "had a couple tough innings. Had some real efficient innings, but the innings that he struggled, they put up some crooked numbers, got some good swings off him."
The Rangers scored three runs in the second. Shortstop Elvis led off with a single and Choo followed with a run-scoring double. With the infield drawn in, DeShields chopped a ball that bounced over third baseman Nolan Arenado for a two-run single.
Choo led off the fourth with a homer and singled home a run in the fifth, when the Rangers added a second run on pitcher Yohan Flande's throwing error. Fielder homered of Flande in the sixth, and the Rangers tacked on single runs against Brothers in the eighth and ninth.
The Rockies were shut out at home for the first time since July 4, 2014.
The Rangers banged out 17 hits, eight for extra bases. DeShields tripled in the eighth. He came up three batters after Choo completed his cycle but struck out against Rafael Betancourt. DeShields said Rangers manager Jeff Banister gave him some advice about hitting a home run.
"He said, 'Don't try to. If it happens it happens,'" DeShields said. "My last at-bat I should have taken a chance. I didn't, I was beating myself up about it. We got the win. That's all that matters."
NOTES: Rockies SS Troy Tulowitzki went 0-for-4, ending his on-base streak at 41 consecutive games, tied for the second longest in Rockies history. ... RF Shin-Soo Choo's cycle was the 13th at Coors Field, the sixth by a Rockies opponent there and the first since Scott Hairston of the Mets on April 27, 2012. The last player to hit for the cycle at Coors Field was Michael Cuddyer of the Rockies on Aug. 17, 2014. It was the eighth cycle in Rangers history and first since Alex Rios on Sept. 23, 2013, against Houston. ... Rockies 2B DJ LeMahieu singled in the fifth inning, extending his hitting streak to 12 games. ... Rangers LHP Derek Holland (left shoulder strain) threw a 35-pitch simulated game, his first since getting injured in April. ... An MRI exam showed that Rockies RHP Chad Bettis (right elbow inflammation) has no structural damage in his elbow. ... Rockies RHP David Hale (left groin strain) threw 25 pitches in a bullpen session, his second since going on the disabled list July 10.