Diamond (5-1) scattered seven hits, didn't issue a walk and struck out five for the Twins, who clinched their fourth consecutive series with the one-sided victory at a hot, humid Target Field.
The second-year left-hander tossed 64 of his 89 pitches for strikes as the Twins won for the sixth time in seven games overall.
Trevor Plouffe's two-run double highlighted a six-run fourth inning and he later added a solo homer to pace Minnesota's offense.
Cubs starter Jeff Samardzija (5-4) was pounded for eight runs on nine hits over 3 2/3 innings.
Alfonso Soriano smacked his third homer in two days, connecting on a two-run shot for Chicago.