Lough's two-run double in the fourth inning put the Royals ahead 4-1 and his solo shot in the eighth off Minnesota's Jared Burton (1-5) broke a 7-7 tie, putting Kansas City ahead to stay.
It was Eric Hosmer's bases-empty homer in the top of the ninth for a 9-7 lead, however, that turned out to be the decisive run for the Royals, who earned a split in the four-game series.
Johnny Giavotella went 3-for-4 with two run-scoring singles for the Royals.
Aaron Crow (5-3) notched the win after blanking the Twins over 1 2/3 innings of relief work.
Minnesota's Trevor Plouffe pounded a solo homer in bottom of the ninth, pulling the Twins within a run, but Greg Holland struck out the next three batters to rack up his 17th save.