Guthrie overcame a shaky start in which he gave up a home run to Rangers shortstop Elvis Andrus in the first inning and a RBI double to first baseman Mitch Moreland in the second. He didn't allow another run from that point, throwing seven innings and scattering five hits and two walks while ringing up five strikeouts in 102 pitches.
Shortstop Alcides Escobar and catcher Salvador Perez each knocked in RBI doubles for the Royals, while left fielder Alex Gordon and second baseman Johnny Giavotella both launched homers to pace a Kansas City offense that piled up 11 hits.
Giavotella's home run, coming off of pitcher Roy Oswalt in the sixth inning, was his first of the season.
Rangers starter Matt Harrison was chased from the game after 4.2 innings, allowing eight hits and five runs (three earned).
Kansas City reliever Greg Holland picked up his 11th save of the season, pitching a scoreless ninth.
Head over to Royals Review for more Kansas City baseball coverage, and check out Lone Star Ball for more on the Rangers. Also visit Baseball Nation for even more news and analysis from around the league.