Models of blazar jets, which explain observations of their photon spectra, typically predict too few neutrinos to be possibly seen by existing telescopes. In particular, they fall short in reproducing the first neutrino ever detected from a blazar, TXS $0506+056$, by IceCube in 2017. We predict larger neutrino fluxes by using the same jet models, extended to include deep inelastic scatterings between protons within the jets and sub-GeV dark matter (DM) around the central black holes of blazars. In this way we succeed in explaining neutrino observations of TXS $0506+056$, for DM parameters allowed by all laboratory, direct, and indirect searches. Our proposal will be tested by DM searches, as well as by the observation of more neutrinos from blazars. Our findings motivate one to implement DM-nuclei interactions in jet models and to improve our knowledge of DM spikes around active galactic nuclei.

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• Cosmic rays & astroparticles
• Particle dark matter
• Neutrinos