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Selective vibrational energy transfer between molecules in the liquid phase, a difficult process hampered by weak intermolecular forces, is achieved through polaritons formed by strong coupling between cavity photon modes and donor and acceptor molecules. Using pump-probe and two-dimensional infrared spectroscopy, we found that the excitation of the upper polariton, which is composed mostly of donors, can efficiently relax to the acceptors within ~5 picoseconds. The energy-transfer efficiency can be further enhanced by increasing the cavity lifetime, suggesting that the energy transfer is a polaritonic process. This vibrational energy-transfer pathway opens doors for applications in remote chemistry, sensing mechanisms, and vibrational polariton condensation.