Kinsler's solo home run in the first inning put the Rangers ahead for good and, after the Rangers put two runners on with none out in the second, Moreland blasted a pitch 463 feet to right field -- the third-longest homer in the history of Rangers Ballpark.
Kinsler added a bases-clearing triple, finishing 3-for-5, while Nelson Cruz and Geovany Soto each added an RBI as the American League West-leading Rangers clinched their four-game series and won for the seventh time in eight contests overall.
Ryan Dempster (3-1) notched a victory in his second straight start, yielding two runs on eight hits over six innings. He walked two and struck out seven.
Twins starter Brian Duensing (3-9) was rocked for nine runs on 10 hits in just 2 1/3 innings.
Justin Morneau went 4-for-4 with a solo homer for Minnesota, which dropped its fifth straight.