Feldman (12-4) worked out of trouble several times after allowing a first-inning run in winning his third straight start. The right-hander allowed seven hits and struck out six to improve to 8-1 with a 3.33 ERA in 10 road starts this season.
Hamilton's double off Jeremy Sowers (4-8) gave the Rangers a 2-1 lead.
Texas won five and lost five during the team's ten game road trip.
The Rangers return to Arlington for a weekend series against the Boston Red Sox.