Harrison, who missed almost all of last season with a herniated disk in his lower back, gave up four runs in the first, then came back with two clean innings in the second and third. He gave up singles in both, but got out of trouble with a pair of double-play grounders.
"When I was sitting there thinking about it, the first inning I was trying too hard, gripping the ball too hard and trying to throw it 100 miles per hour," Harrison said. "The two innings I was focused and relaxed. I loosened my grip and had better sink down in the zone. I had a little bit too much adrenaline instead of focusing and relaxing and making my pitches."
Harrison finished with 49 pitches in only his second A game of the spring. He will start the season on the disabled list while completing his recovery from two back operations and one surgery on his right non-throwing shoulder. His next outing will be for Double A Frisco on Wednesday.
He will likely need four more starts on medical rehabilitation assignment before he is an option at the Major League level. The earliest he could realistically return to the Rangers rotation is on April 23.
"It's taking a little more time than I thought," Harrison said.
Jerome Williams, who is headed for the Astros bullpen, started and allowed only a solo home run by Adrian Beltre in three innings. Williams had allowed 12 runs, eight earned, over his three previous outings. Brad Peacock followed with three scoreless innings, allowing three hits and striking out four.
Nick Martinez followed Harrison to the mound and allowed one run through five innings. He is scheduled to make his first Major League start on April 5 against the Rays.
"I wasn't as nervous as I thought I would be," Martinez said. "I feel prepared and ready to go. I located my fastball and that opened up everything else for my other pitches."
The Astros and Rangers will play again on Saturday at the Alamodome, which has been converted from football stadium to baseball ballpark.
"They did a tremendous job with the field," Astros manager Bo Porter said. "Even though right field is a little bit short, the length of the grass held the ground balls down so it kind of evens out a little bit. Overall I think they did a tremendous job with the facility as a whole."
Up next: The Rangers close out Spring Training with their final exhibition game against the Astros at 1 p.m. CT on Saturday at the Alamodome in San Antonio. Joe Saunders will make his last start of the spring in preparation for pitching against the Rays on Friday. He is the Rangers fourth starter.
T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, and follow him on Twitter @Sullivan_Ranger. This story was not subject to the approval of Major League Baseball or its clubs.