We present a Monte Carlo method for direct incorporation of nuclear inputs in primordial nucleosynthesis calculations. This method is intended to remedy shortcomings of current error estimation, by eliminating intermediate data evaluations and working directly with experimental data, allowing error estimation based solely on published experimental uncertainties. This technique also allows simple incorporation of new data and reduction of errors with the introduction of more precise data. Application of our method indicates that previous error estimates on the calculated abundances were too large by as much as a factor of three. Since uncertainties in the BBN calculation currently dominate inferences drawn from light-element abundances, the re-estimated errors have important consequences for cosmic baryon density, neutrino physics, and lithium depletion in halo stars. Our direct method allows detailed discussion of the status of the nuclear inputs, by identifying clearly the places where improved cross section measurements would be most useful. 26.35.+c, 98.80.Ft