Griffin (2-0) held the Astros to two runs and four hits over six innings to improve to 4-0 lifetime against Houston, which has now lost 10 straight in Globe Life Park.
Griffin found trouble in the first but limited Houston's big-inning prospects after giving up consecutive doubles to Jose Altuve and George Springer to start the game, a matter of bad pitch execution, he said. A one-out walk to Colby Rasmus put runners on first and second.
But Griffin retired Tyler White by flyout and Preston Tucker on a meek groundout to get out of the inning.
After being staked a two-run lead with Ian Desmond's homer in the Texas first, Griffin followed with shutdown innings in the second and third, retiring eight consecutive before Rasmus touched him for a leadoff homer in the fourth.
The right-hander set down eight of the last 11 hitters he faced.
"He looked pretty fresh," said manager Jeff Banister of Griffin, who was working on seven days' rest. "A little more extension, a little more life on the fastball, cutter had a little more bite to it. That slow breaking ball, you never know when he's going to throw it and he drops it in there. It keeps hitters [out of] rhythm."
The start was a continuation of a good start to the season for the Rangers rotation.
With Griffin's outing, Texas starters have pitched at least five innings in each of the team's first 16 games, the second-longest streak to open a season in Rangers history. The 2012 team had 18 consecutive. The Rangers' 11 quality starts are tied for second-most in the AL.
Success from Griffin is like manna from heaven for the Rangers. He hadn't pitched in two years after Tommy John surgery in April 2014.
His only professional action of the past two seasons came over four games for Class A Advanced Stockton and Triple-A Nashville last June. It was there that he suffered a shoulder strain and was shut down essentially for a second straight year.
The Rangers signed him as a Minor League free agent in January. Griffin earned the fifth spot in the rotation out of Spring Training, though roster logistics had him at Triple-A on Opening Day.
"I felt like I was able to spin the ball the way I wanted to. I was able to hit my spots better. Better lines where I was trying to throw my fastball," said Griffin, who threw 108 pitches (71 for strikes). "Everything was just better today."