Sub-diffraction microscopy enables bio-imaging with unprecedented clarity. However, most super-resolution methods require complex, costly purpose-built systems, involve image post-processing and struggle with sub-diffraction imaging in 3D. Here, we realize a conceptually different super-resolution approach which circumvents these limitations and enables 3D sub-diffraction imaging on conventional confocal microscopes. We refer to it as super-linear excitation-emission (SEE) microscopy, as it relies on markers with super-linear dependence of the emission on the excitation power. Super-linear markers proposed here are upconversion nanoparticles of NaYF4, doped with 20% Yb and unconventionally high 8% Tm, which are conveniently excited in the near-infrared biological window. We develop a computational framework calculating the 3D resolution for any viable scanning beam shape and excitation-emission probe profile. Imaging of colominic acid-coated upconversion nanoparticles endocytosed by neuronal cells, at resolutions twice better than the diffraction limit both in lateral and axial directions, illustrates the applicability of SEE microscopy for sub-cellular biology.