Exceptional field theories yield duality covariant formulations of supergravity. We show that they provide a highly efficient tool to compute the Kaluza-Klein mass spectra associated with compactifications around various background geometries relevant for string theory and holographic applications. This includes geometries with little to no remaining symmetries, hardly accessible to standard methods. As an illustration, we determine the masses of some higher Kaluza-Klein multiplets around warped geometries corresponding to some prominent N=2 supersymmetric anti-de Sitter vacua in maximal supergravity.