Texas, who had blanked the Astros 2-0 in game one of the best-of-seven American League Championship Series on Sunday, jumped on Houston starter Framber Valdez early to take a commanding 4-0 first inning lead at Minute Maid Park.
Marcus Semien scored after a fielding error from Valdez to make it 1-0 before Adolis Garcia's line drive to right field allowed Corey Seager to score.
Mitch Garver then drove in a run to put Texas 3-0 ahead before Nathaniel Lowe singled to left field to send Garcia home for a 4-0 lead.
Houston finally got on the board in the bottom of the second inning when Yordan Alvarez crushed a 420-foot home run to right centre field.
But Texas immediately restored their four-run cushion when Jonah Heim blasted a solo shot to left field in the top of the third to make it 5-1.
The Astros however continued to chip away at the Texas lead, with Alex Bregman's home run in the fourth inning making it 5-2.
Houston then appeared to be poised to hit back again in the fifth inning, loading the bases with no outs to pile the pressure on Texas starter Nathan Eovaldi.
'Turning point'
But Eovaldi rose to the challenge superbly, extricating himself from the jam to end the inning with Houston unable to cash in.
"That was the turning point in the game," Rangers manager Bruce Bochy said of Eovaldi, who finished with nine strikeouts through six innings to claim the win.
"Terrific job by him," Bochy added. "He had good stuff today. He pitched very well."
Houston got within two in the sixth inning after a Michael Brantley double made it 5-3.
Alvarez then swatted his second home run of the game in the eighth to set up a nerve-jangling finale heading into the eighth.
But Texas closer Jose Leclerc took care of business to remove Jeremy Pena, Yainer Diaz and Jose Altuve in quick succession to seal victory. Game three in the series takes place in Arlington, Texas on Wednesday.
The winner of the ALCS will face the winner of the National League Championship Series between the Philadelphia Phillies and the Arizona Diamondbacks in the World Series.
The Phillies - beaten by the Astros in last year's World Series -- launched their bid to return to the Fall Classic with a 5-3 victory over the Diamondbacks on Monday.
The Phillies launched an early offensive onslaught with Kyle Schwarber and Bryce Harper blasting first inning solo home runs before Nick Castellanos crushed a third homer in the second inning to make it 3-0.
Harper and J.T. Realmuto drove in two more runs to make it 5-0 and although Arizona got to within two runs, closer Craig Kimbrel shut it down with the Phillies winning on a double play.
Game two of the NLCS takes place on Tuesday.
