Fister (2-1) earned the win and got Detroit in the win column after the Tigers had dropped the first two games to the defending American League champions.
The series resumes in Detroit Wednesday.
Fister went 7 2/3 innings, allowing two runs on seven hits. He struck out three and did not give up a walk before turning the game over to Joaquin Benoit and Jose Valverde, who closed out the ninth for the save.
Colby Lewis (1-1) was tagged with the loss in the Rangers' first setback since Game 1 of the American League Division Series against Tampa Bay. Lewis was charged with four runs on eight hits over 5 2/3 innings and struck out six.