Willigham's two-run shot in the fourth inning put the Twins ahead for good at 2-1 and Casilla doubled the advantage with a two-run triple in the next frame, later scoring on a single by Ben Revere (3-for-5, two RBI).
Casilla also triggered a five-run sixth with a two-run double, and Minnesota went on to pound the Indians for a second straight night. The Twins defeated the Tribe 11-0 Friday in the first contest of the three-game set.
Samuel Deduno (2-0) overcame five walks issued through seven innings, holding Cleveland to one run on just two hits while striking out six.
Indians starter Justin Masterson (7-9) was rocked for 10 runs (eight earned) on seven hits before being knocked out after 5 2/3 frames.
Carlos Santana smacked a two-run homer for Cleveland, which lost for the third time in four games and fell 5 1/2 games behind the American League Central-leading Chicago White Sox.