Muons can be created in nascent neutron stars (NSs) due to the high electron chemical potentials and the high temperatures. Because of their relatively lower abundance compared to electrons, their role has so far been ignored in numerical simulations of stellar core collapse and NS formation. However, the appearance of muons softens the NS equation of state, triggers faster NS contraction, and thus leads to higher luminosities and mean energies of the emitted neutrinos. This strengthens the postshock heating by neutrinos and can facilitate explosions by the neutrino-driven mechanism.