We demonstrate microwave dressing on ultracold, fermionic 23Na40K ground-state molecules and observe resonant dipolar collisions with cross sections exceeding three times the s-wave unitarity limit. The origin of these collisions 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-channels calculations that agree well with the experimentally observed collision rates. While collisions are observed here as laser-induced loss, microwave dressing on chemically stable molecules trapped in box potentials may enable the creation of strongly interacting dipolar gases of molecules.