The Indians intentionally walked Mitch Moreland to put two runners on with two out in the 11th, and Beltre came in to bat for Alberto Gonzalez.
The Texas slugger then blasted a high pitch from Joe Smith (1-1) 456 feet to straightaway center field, which cleared the shrubbery behind the fence at Progressive Field.
The clout made a winner of Alexi Ogando (1-0), who tossed two scoreless innings as the American League West-leading Rangers broke a three-game skid and evened their series with AL Central-leading Cleveland.
Joe Nathan got the final three outs for his seventh save and Moreland finished 3-for-4 with an RBI.
Asdrubal Cabrera collected four hits with an RBI for Indians, who saw their three-game winning streak snapped.