Jeff Gray came in to pitch and Beltre greeted him with a tie-breaking single.
The next batter, Michael Young, then made it 4-2 with another RBI hit.
Hamilton finished 3-for-5 with an RBI and three runs scored while Nelson Cruz added three hits for the Rangers, who clinched their three-game series at Target Field and improved to 7-2 to start the season.
Robbie Ross (1-0) got the win in relief of Japanese hurler Yu Darvish, who yielded two runs (one earned) on nine hits over 5 2/3 in his second major league start.
Twins starter Nick Blackburn allowed two runs on seven hits before exiting after 5 1/3 innings with shoulder stiffness.
Denard Span went 3-for-5 with an RBI for Minnesota.
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