We address the semi-calibrated relative pose estimation problem where we assume the principal point to be in the center of the image and estimate the focal lengths, relative rotation, and translation of two cameras. We introduce the first minimal solver that requires only a single affine correspondence in conjunction with predicted monocular depth. Recognizing its degeneracy when the correspondence stems from a fronto-parallel plane, we present an alternative solver adept at recovering the correct solution under such circumstances. By integrating these methods within the GC-RANSAC framework, we show they surpass standard approaches, delivering more accurate poses at comparable runtimes across large-scale, publicly available indoor and outdoor datasets. The code will be public.