With the Twins leading 5-2 in the sixth, Denard Span got aboard on a bunt single and Revere followed by lining a 1-1 pitch into the right-field corner for a three-bagger, giving Minnesota a four-run lead.
Revere went 4-for-4 with three runs scored for Minnesota, which salvaged one win in a four-game series.
Cole De Vries (3-5) earned the victory, yielding two runs (one earned) on three hits over five innings. The rookie didn't issue a walk and struck out five.
Scott Feldman (6-10) was tagged for 10 hits over 5 2/3 frames, allowing six runs (five earned) for American League West-leading Texas.
Hamilton finished with four RBI, giving him an MLB-best 111 for the season.