Cruz finished 3-for-4, belting a solo homer in the fourth and a go-ahead two-run shot in the seventh. He added a run-scoring double in the seventh for an 8-6 lead, which turned out to be the decisive tally.
Pierzynski, meanwhile, launched a two-run shot in the second inning to open the scoring and supplied a game-tying two-bagger for the Rangers, who took the first of a key four-game American League West series.
Neal Cotts (3-1) earned the victory with 2 1/3 scoreless relief frames after Texas starter Nick Tepesch was roughed up for six runs over 3 2/3 innings.
Joe Nathan picked up his 21st save despite yielding a run in ninth for the second-place Rangers, who pulled two games behind AL West-leading Oakland.
Jesse Chavez (1-1) took the loss for Oakland, which fell for the third time in four games.