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We present an analytic, perturbative solution that describes dynamical black holes in slow-roll inflation with a general potential. It is shown that the spacetime evolves quasi-statically through a sequence of quasi-Schwarzchild-deSitter metrics with time dependent cosmological constant and mass parameters, such that the cosmological constant is instanteously equal to the value of the scalar potential.  The areas of the black hole and cosmological horizons each increase in time as the effective cosmological constant decreases, and the the factional area increase is proportional to the fractional change of the cosmological constant, times a geometrical factor. For black holes ranging in size from much smaller than to comparable to the cosmological horizon, the pre-factor varies from very small to order one. The change in the horizon areas happens in such a way that the first law of thermodynamics is obeyed between successive time steps.