Kluber, the No. 2 starter in the Indians' rotation, allowed two runs on five hits in seven innings in Cleveland's 3-2 victory over a Diamondbacks' split-squad on Thursday.
Kluber blanked Arizona for six innings before being tagged for a pair of runs in the seventh. He struck out seven and walked one.
Miley, the starter in the Diamondbacks' season-opening 3-1 loss to Clayton Kershaw and the Los Angeles Dodgers in Australia, gave up three runs on seven hits in 4 2-3 innings, walking one and hitting a batter.
Both teams have exhibition games Friday and Saturday. Arizona plays the Chicago Cubs at Phoenix's Chase Field, the Indians are at San Diego.