Kubel's run-scoring single in the fifth inning put the D-Backs ahead 2-0 and his two-run double during a five-run sixth helped put the game away for Arizona.
Willie Bloomquist and Gerardo Parra each added two hits and an RBI and Cody Ransom delivered a two-run double as Arizona pounded out 14 hits to finish with three wins in their four-game set against the Marlins.
Miley (3-0) took a no-hitter into the sixth inning, when John Buck notched Miami's only hit off him. The left-hander ended up yielding one unearned run while walking two and fanning six.
Marlins starter Josh Johnson (0-3) was tagged for five runs on 10 hits in an outing that lasted only 5 1/3 frames.
Giancarlo Stanton belted a three-run homer and finished with four RBI for Miami, which fell to its seventh loss in eight games.