To identify the superconducting gap structure in URu(2)Si(2), we perform field-angle-dependent specific heat measurements for the two principal orientations in addition to field rotations, and a theoretical analysis based on microscopic calculations. The Sommerfeld coefficient gamma(H)'s in the mixed state exhibit a distinctly different field dependence. This comes from point nodes and the substantial Pauli paramagnetic effect of URu(2)Si(2). These two features combined give rise to a consistent picture of superconducting properties, including a possible first order transition of H(c2) at low temperatures.