We demonstrate microwave dressing on ultracold, fermionic ^{23}Na^{40}K ground-state molecules and observe resonant dipolar collisions with cross sections exceeding 3 times the s-wave unitarity limit. The origin of these interactions is the resonant alignment of the approaching molecules' dipoles along the intermolecular axis, which leads to strong attraction. We explain our observations with a conceptually simple two-state picture based on the Condon approximation. Furthermore, we perform coupled-channel calculations that agree well with the experimentally observed collision rates. The resonant microwave-induced collisions found here enable controlled, strong interactions between molecules, of immediate use for experiments in optical lattices.