  We propose a novel and simple mechanism where sizable effects of non-standard
interactions (NSI) in neutrino propagation are induced from the mixing between
an electrophilic second Higgs doublet and a charged singlet. The mixing arises
from a dimensionful coupling of the scalar doublet and singlet to the standard
model Higgs boson. In light of the small mass, the light mass eigenstate from
the doublet-singlet mixing can generate much larger NSI than those induced by
the heavy eigenstate. We show that a sizable NSI $\varepsilon_{e\tau}$ ($\sim
0.3$) can be attained without being excluded by a variety of experimental
constraints. Furthermore, we demonstrate that NSI can mimic effects of the
Dirac CP phase in the neutrino mixing matrix but they can potentially be
disentangled by future long-baseline neutrino experiments, such as the Deep
Underground Neutrino Experiment (DUNE).
