Singlet pairing in a Fermi superfluid is frustrated when the amounts of fermions of each pairing partner are unequal. The resulting "imbalanced superfluid" has been realized experimentally for ultracold atomic gases with s-wave interactions. Inspired by high-temperature superconductivity, we investigate the case of d-wave interactions and find marked differences from the s-wave superfluid. Whereas s-wave imbalanced Fermi gases tend to phase separate in real space, in a balanced condensate and an imbalanced normal halo, we show that the d-wave gas can phase separate in reciprocal space so that imbalance and superfluidity can coexist spatially. We show that the mechanism explaining this property is the creation of polarized excitations in the nodes of the gap. The Sarma mechanism, present only at nonzero temperatures for the s-wave case, is still applicable in the temperature zero limit for the d-wave case. As a result, the d-wave BCS superfluid is more robust with respect to imbalance and a region of the phase diagram can be identified where the s-wave BCS superfluidity is suppressed whereas the d-wave superfluidity is not. When these results are extended into the Bose-Einstein condensate limit of strongly bound molecules, the symmetry of the order parameter matters less. The effects of fluctuations beyond mean field is taken into account in the calculation of the structure factor and the critical temperature. The poles of the structure factor (corresponding to bound molecular states) are less damped in the d-wave case as compared to that in s wave. On the BCS side of the unitarity limit, the critical temperature T-c follows the temperature T-* corresponding to the pair binding energy and as such will also be more robust against imbalance. Possible routes for the experimental observation of the d-wave superfluidity have been discussed.