Beltre singled in the game's first run in the opening inning and scored in the seventh on a base hit by Michael Young to give the Rangers a 5-1 lead. Beltre is heading into the final month of the season with a .316 batting average.
Young had two RBI overall and Ian Kinsler doubled in a run in what was the third Texas win in four games.
Ryan Dempster (4-1) allowed a lone unearned run on two hits with three walks and seven strikeouts in six innings to get the win.
Casey Kotchman hit a two-run homer for the Indians in the ninth. It was the 24th loss in August for the Indians, the most setbacks they have had in a single month since 1914.
Ubaldo Jimenez (9-14) took the loss, giving up four runs on eight hits in 5 2/3.