Guthrie (12-7) tossed his second career shutout and second of the year -- he also blanked the Chicago White Sox May 4. The right-hander scattered four hits, issued one walk and struck out seven in the 106-pitch gem.
Hosmer (3-for-5) delivered a two-run single during a six-run uprising in the second inning and pounded a three-run homer in sixth as the Royals scored their fourth win over the Twins in a week.
Mike Moustakas went 4-for-5 with two RBI and Alcides Escobar provided two hits with two runs batted in for Kansas City, which posted is most one-sided shutout triumph since 1987.
Minnesota's Kevin Correia (7-8) was torched for six runs on seven hits, lasting just two full innings as the Twins fell in the opener of a three-game series.