Exact exchange is an important constituent in many state-of-the-art approximations to the exchange-correlation (xc) functional of Kohn-Sham DFT. However, its evaluation can be computationally intensive, which can be particularly prohibitive in DFT-based molecular dynamics (MD) simulations, often restricted to semilocal functionals. We derive a scheme based on the formal coordinate scaling properties of the exact xc functional that allows for a substantial reduction of the cost of the evaluation of both the exact exchange energy and potential. We show that within a plane-wave/pseudopotential framework, excellent accuracy is retained, while speed ups from up to ∼6 can be reached. The coordinate scaling thus accelerates hybrid-functional-based first-principles MD simulations by nearly one order of magnitude.