Neutral-atom tweezer arrays support scalable quantum information processing. Dual-species ⁸⁷Rb--¹⁷¹Yb arrays combine long-lived ytterbium nuclear-spin data qubits with fast, species-selective rubidium ancilla control and readout. However, realizing interspecies gates without inducing destructive Stark mixing in divalent atoms remains an outstanding problem. Here, we identify an optically accessible S+S↔ P+P Förster resonance at zero electric field, providing strong dipole-dipole exchange at array pitch. Using a shaped optical pulse under finite control response, we demonstrate a 0.36 μs exchange-assisted controlled-Z gate with an intrinsic fidelity of 99.91%, remaining above 99.85% under bounded perturbations. We also identify an auxiliary repulsive van der Waals channel, providing a comprehensive toolbox for hybrid quantum processors.