Gordon's blast with Alcides Escobar aboard in the fifth inning broke a 2-2 tie and Salvador Perez added a run-scoring double later in the frame to ice the victory for Kansas City.
Guthrie (4-3) yielded a pair of runs on five hits over seven innings, walking two and striking out five as the Royals evened their four-game series at one win apiece.
Matt Harrison (15-9) was tagged with the loss, surrendering five runs (three earned) on eight hits over 4 2/3 innings for American League West-leading Texas.
Elvis Andrus homered for the Rangers.
Celebrity Families of 2014 [PHOTOS]