Cruz and Michael Young each drew walks from Brayan Villarreal (3-3) to lead off the ninth in a 1-1 tie game.
Cruz beat the throw home for the winning tally and also drove in the Rangers' other run with a third-inning single.
The late rally made a winner of Mike Adams (2-3), who worked out of a bases-loaded, one-out jam in the top of the ninth.
Derek Holland struck out nine over 7 2/3 innings of one-run ball for the American League West-leading Rangers, who evened the three-game series.
Detroit starter Justin Verlander fanned eight over seven solid innings, during which he yielded one run on seven hits and didn't issue a walk.
Austin Jackson homered for the second-place Tigers, who remained one game behind American League Central-leading Chicago White Sox.