Reconfigurable intelligent surface (RIS)-aided localization in the radiating near-field requires range-aware spherical-wave models, which inherently couple angles and ranges and thus complicate accurate 3D positioning. Using the Fresnel approximation, we show that the RIS response can be expressed as the element-wise product of a 2D far-field steering vector and a range-dependent quadratic-phase chirp. By modeling these chirp components within a low-dimensional subspace, we reformulate the joint recovery of azimuth, elevation, and range under a 2D super-resolution framework, resulting in a 2D atomic norm minimization (2D-ANM) problem. Solving this via semi-definite programming (SDP) yields gridless azimuth-elevation estimation and high-accuracy range recovery. Simulations demonstrate accurate 3D localization and enhanced robustness of the proposed scheme, compared with subspace and compressive sensing methods.