Beltre opened the scoring with a solo shot in the second inning, then added a three-run blast in the fifth to hand Texas a 5-2 lead.
The Rangers third baseman added an RBI single in the ninth to cap the scoring as Texas took a second straight victory in its four-game series at Camden Yards.
Martin Perez (3-1) was the beneficiary of Beltre's big night, gaining the win despite allowing four runs (two earned) on six hits over six innings for second-place Texas, which came into the contest trailing American League West-leading Oakland by 1/2-game.
Baltimore's Zach Britton (2-3) was tagged with the loss, surrendering five runs on eight hits over five full frames.
J.J. Hardy drove in a pair of runs and Manny Machado homered for the Orioles, who fell to 2-6 in July.