Perez (1-0), a 21-year-old Venezuelan, controlled the A's on two runs over 5 1/3 innings, surrendering six hits and a walk while striking out five as Texas won its fifth straight.
The left-hander, regarded as the Rangers' top pitching prospect, was making only his second big-league appearance after his debut in a relief role Wednesday.
The Rangers were trailing 2-1 in the fifth when Ian Kinsler's two-run single gave them the lead and Hamilton then put the contest away with a three-run shot off A's starter Tommy Milone (8-6).
All five Texas runs in the frame were unearned following errors by Oakland third baseman Brandon Inge and shortstop Brandon Hicks.
Milone ended up allowing six runs (one earned) on six hits over five frames as the A's dropped to 0-3 in their four-game series against the Rangers.
Chris Carter homered in Oakland's loss.