Guthrie (8-6) registered his first win in nearly a month, yielding six hits and a walk while striking out three. The right-hander waited out a hour-long rain delay en route to the victory.
Butler's blast in the second broke a scoreless tie and the Royals never trailed after that.
New York's Phil Hughes (4-8) was saddled with the loss, yielding a pair of runs on four hits over four frames.
Lyle Overbay socked a bases-empty homer for the Yankees.