Context. Many massive stars have nearby companions whose presence hamper their characterization through spectroscopy. Aims. We want to obtain spatially resolved spectroscopy of close massive visual binaries to derive their spectral types. Methods. We obtained a large number of short long-slit spectroscopic exposures of five close binaries under good seeing conditions. We selected those with the best characteristics, extracted the spectra using multiple-profile fitting, and combined the results to derive spatially separated spectra. Results. We demonstrate the usefulness of Lucky Spectroscopy by presenting the spatially resolved spectra of the components of each system, in two cases with separations of only ~0.′′3. Those are δ Ori Aa+Ab (resolved in the optical for the first time) and σ Ori AaAb+B (first time ever resolved). We also spatially resolve 15 Mon AaAb+B, ζ Ori AaAb+B (both previously resolved with GOSSS, the Galactic O-Star Spectroscopic Survey), and η Ori AaAb+B, a system with two spectroscopic B+B binaries and a fifth visual component. The systems have in common that they are composed of an inner pair of slow rotators orbited by one or more fast rotators, a characteristic that could have consequences for the theories of massive star formation.