With the score tied 5-5 in the fifth, Elvis Andrus and Josh Hamilton led off with singles and Beltre followed with a third straight hit off Rays starter David Price (16-5), providing the winning margin.
Beltre finished 3-for-3 with a solo homer -- going back-to-back with Nelson Cruz in the second inning -- and added a two-run double in the next frame.
Starter Derek Holland (9-6) allowed five runs (three earned) on six hits over six innings before the Rangers' bullpen took over.
Price was roughed up for 10 hits over four full innings, yielding six runs.
Evan Longoria belted a two-run homer and B.J Upton also knocked in a pair for the AL wild card-leading Rays, who dropped the opener of a three-game series.