Entanglement has long stood as one of the characteristic features of quantum mechanics, yet recent developments have emphasized the importance of quantumness beyond entanglement for quantum foundations and technologies. We demonstrate that entanglement cannot entirely represent the figure of merit in worst-case scenario quantum interferometry, where quantum probes are used to estimate the phase imprinted by a least informative Hamiltonian acting on one arm of the interferometer. This is shown by defining a suitable bipartite entanglement monotone and proving that it never exceeds the interferometric power, which relies on more general quantum correlations beyond entanglement and captures the relevant resource in this setting. We then prove that the interferometric power can never increase when local commutativity preserving operations are applied to qubit probes, an important step to validate such a quantity as a genuine quantum correlations monotone. These findings are supported experimentally using a room temperature nuclear magnetic resonance setup, in which two-qubit states with extremal interferometric power at fixed entanglement are produced and characterized. ; Comment: 10 pages, 2 figures, 1 table