The Rangers' Game 1 win was their third straight at home in the ALCS, dating back to 2010.
Game 1 was the Tigers' first loss in the ALCS since 1987.
Detroit catcher Alex Avila went 0-for-4 and is 1-for-20 in the postseason.
The Tigers were 6-3 against the Rangers in the regular season, including a 2-1 record in Arlington.
Detroit center fielder Austin Jackson has 11 strikeouts in 21 postseason at-bats, including three whiffs in the ALCS opener.
Game 1 was the fourth straight win for the Rangers.
Texas closer Neftali Feliz became the seventh pitcher to record three saves in a Division Series. He recorded his fourth save of the postseason in Game 1.
Detroit left fielder Ryan Raburn's two walks in Game 1 gave him his first multiwalk game of the season.
Both clubs had a negative run differential in their ALDS wins.
Alexi Ogando entered the ALCS with a 3-0 record and 1.54 ERA in six career games against the Tigers. He pitched two shutout innings with three strikeouts in Game 1.
The team that lost Game 1 has won seven of the past 11 ALCS, including the Rangers last season.
Chris Vannini is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.