Keep in mind that Michael probably had a fairly lengthy "apprenticeship" under Vito between the time he returned from Sicily until Vito's death. That was enough time for him to establish himself as a force to be reckoned with. And, though we don't see it, I'm sure he was smart enough to buy loyalty in the same ways Vito did: by rewarding loyalty.

As we saw at the end: Michael was deliberately testing the loyalty of the two caporegimes. That risk worked out in his favor.