  We construct UV-complete models for non-standard neutrino interactions
mediated by a sub-GeV gauge boson Z' coupled to baryon number $B$ or $B-L$. A
flavor-dependent Z' coupling to neutrinos is induced by mixing a U(1)'-charged
Dirac fermion with the active neutrinos, naturally suppressing flavor violation
or non-universality of the charged leptons to the loop level. We show that
these models can give rise to large flavor-conserving as well as
flavor-violating non-standard neutral-current neutrino interactions potentially
observable in current or future oscillation experiments such as DUNE without
being in conflict with other constraints such as neutrino scattering or
lepton-flavor-violating decays. In particular, the LMA-Dark solution to the
solar-neutrino anomaly can be obtained for $U(1)_B$, but not for $U(1)_{B-L}$.
