Hamilton, slowed this season by shoulder surgery, was 0 for 3 with two strikeouts and a walk, and scored a run.
The 2010 AL MVP came up with runners on first and second and two outs in the seventh inning with the score 8-all. He hit an easy tapper back to pitcher Zach McAllister, whose throw was well over the head of first baseman Carlos Santana for a two-base error.
Hamilton was traded from the Angels back to Texas in late April.
Prince Fielder hit his fourth home run in four games for the Rangers. He hit an RBI single that tied it earlier in the seventh.
The Indians had won six in a row.