The Royals, who had not scored in the first two innings in their first seven games, sent nine to the plate in a five-run first. Mike Pelfrey (1-1) gave up hits to the first five batters he faced.
Joe Mauer, Josh Willingham and Eduardo Escobar - the first of his career - each hit solo homers to keep the Twins close.
Guthrie (2-0) improved to 7-0 in his past 13 starts dating to last Aug. 8. Guthrie, who has a 2.37 ERA during the stretch, allowed four runs on six hits, including the three home runs, in 6 2/3 innings.
Greg Holland picked up the save, but not before walking two and giving up a single to Escobar, his third hit, to load the bases. Holland struck out Mauer to end the game, logging his second save in three chances.
After Mauer gave the Twins a 1-0 lead in the first,
Alex Gordon and Escobar got things started for the Royals with singles. Billy Butler doubled down the left-field line to score Gordon,
Mike Moustakas singled home Escobar, and
Salvador Perez doubled home Butler.
Eric Hosmer's groundout scored Moustakas, and
Lorenzo Cain's two-out single scored Perez.
Pelfrey, who made only three starts last season for the New York Mets before needing reconstructive elbow surgery on May 1, was chased after two innings, allowing six runs on eight hits. He went to Wichita Heights High School and Wichita State, about 200 miles from Kauffman Stadium.
Escobar drove in a run in the second to make it 5-2, but Gordon opened the Royals' half of the second with a triple and scored on Alcides Escobar's single.
After Willingham's homer in the third, the Royals scored their final run on Jeff Francoeur's double that scored Hosmer.
Eduardo Escobar went deep in the fifth to cap the scoring.
The Royals, who had a 12-game losing streak last April, have won three straight and five of six.
Notes: Twins rookie CF Aaron Hicks, who had never played above Double-A before this season, was not in the starting lineup after only two singles in 30 at-bats and striking out 13 times. ... Moustakas' fielding miscue in the fifth inning was the Royals' first of the season, ending an errorless streak of 64 2/3 innings.