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.