A stable inversion method of determining molecular potentials from a finite number of spectroscopic data is presented. Molecular inverse problems are often underdetermined, unstable, and nonlinear. Specifically, the measured spectra contains only partial information of the sought-after potential and even a small error in the data may cause a large variation in the inverted solution. Moreover, the underlying potential is a complicated nonlinear functional of the spectral data. The inversion algorithm, based on the Tikhonov regularization method, resolves all of the above predicaments and yields accurate sought-after potentials with proper analytic properties. The method is applied to extract two-dimensional Ar-OH(A(2) Sigma(+), nu=0) potential energy surfaces from the rotational-vibrational spectral data. Two versions of the recovered potential energy surfaces ate obtained using two slightly different sets of rovibrational data. These two potentials are basically equivalent, except in the regions to which the data are insensitive, and possess physically acceptable smooth features with the correct long-range behavior. Both recovered potentials reproduce the observed spectra, the estimated rotational constants, and the binding energy within the experimental accuracy.