Point cloud registration remains a challenging and open task in computer vision, especially for correspondence-free point cloud registration methods. This paper presents a classification-guided registration, which is a robust correspondence-free point cloud registration framework that achieves gradual and precise registration through a two-stage pipeline: classification-guided coarse pose estimation and kernel-optimized fine-grained refinement. To address large angular misalignments, the first stage employs an equivariant network with a classification-guided module, enhanced by conditional adversarial domain adaptation, to predict reliable coarse rotations robust to translational perturbations. In the second stage, we improve the reproducing kernel Hilbert space (RKHS) distance metric in the kernel evaluation module, enabling better alignment of point cloud features and enhanced robustness against noise and outliers. Extensive experiments on synthetic datasets (ModelNet40) and real-world datasets (3DMatch & 3DLoMatch) demonstrate that the CGReg method outperforms classical methods and the state-of-the-art correspondence-free methods. Its advantage is particularly evident in challenging scenarios with large angles or low overlaps.