Abstract Extraordinary optical transmission (EOT) is a hallmark of surface plasmons and a precursor to nanoplasmonics and metamaterials. However, to the best of our knowledge, this effect has never been topologically protected in three dimensions, leaving it vulnerable to structural imperfections, nonlocal effects, and backreflections. We report broadband, three-dimensional unidirectional structures that allow for EOT (normalized transmission > 1) through deep-subdiffractional single holes, immune to these deleterious effects. These structures avoid unnecessary propagation losses and achieve maximum transmission through a single hole, limited only by unavoidable dissipative losses. In the limit of vanishing losses, the transmission through a deep-subdiffractional hole can approach unity, significantly surpassing existing devices, and rivaling the performance of negative-index ‘perfect’ lenses. The topological stability of these structures renders them robust against surface roughness, defects, and nonlocality, without the need for elaborate meta-structures or tapering.