We carried Out three-dimensional global resistive magnetohydrodynamic simulations of the cooling instability in optically thin hot black hole accretion flows by assuming bremsstrahlung cooling. General relativistic effects are Simulated using the pseudo-Newtonian potential. The cooling instability grows when the density of the accretion disk becomes sufficiently large. We found that as the instability grows the accretion flow changes from an optically thin, hot, gas pressure-supported state (low/hard state) to a cooler, magnetically Supported, quasi-steady state. During this transition, the magnetic pressure exceeds the gas pressure because the disk shrinks in the vertical direction while almost conserving the toroidal magnetic flux. Since further vertical contraction of the disk is suppressed by magnetic pressure, the cool disk stays in an optically thin, spectrally hard state. The magnetically Supported disk exists for a time scale much longer than the thermal time scale, and comparable to the accretion time scale. We examined the stability of the magnetically supported disk analytically, assuming that the toroidal magnetic flux is conserved, and found it to be thermally and secularly stable. Our findings may explain why black hole candidates stay in luminous, hard state even when their luminosity exceeds the threshold for the onset of the cooling instability.