One of the open challenges of spintronics is to control the spin relaxation mechanisms. Layered metal-halide perovskites are an emerging class of semiconductors which possess a soft crystal lattice that strongly couples electronic and vibrational states and show promise for spintronic applications. Here, we investigate the impact of such strong coupling on the spin relaxation of excitons in the layered perovskite BA2FAPbI7 using a combination of cryogenic Faraday rotation and transient absorption spectroscopy. We report an unexpected increase of the spin lifetime by two orders of magnitude at 77 K under photoexcitation with photon energy in excess of the exciton absorption peak, and thus demonstrate optical control over the dominant spin relaxation mechanism. We attribute this control to strong coupling between excitons and optically excited phonons, which form polaronic states with reduced electron-hole wave function overlap that protect the exciton spin memory. Our insights highlight the special role of exciton-lattice interactions on the spin physics in the layered perovskites and provide a novel opportunity for optical spin control.