At long-baseline neutrino experiments, neutral-current (NC) events accumulate in large numbers but are seldom exploited for new physics searches. We demonstrate their potential using nonstandard neutrino interactions (NSI) with quarks as a case study. Charged-current (CC) analyses constrain NSI through matter effects on neutrino propagation, which probe almost exclusively the isoscalar combination of up- and down-quark couplings; the orthogonal isovector combination is suppressed by a factor of ~100. Because NSI also modify NC cross sections in a flavor-dependent way, NC events become sensitive to oscillations: the far-to-near detector ratio acquires a dependence on the beam’s flavor composition that probes both isoscalar and isovector couplings with comparable weight. Using existing NOvA data and DUNE projections, we derive the first bounded constraints on isovector NSI from a long-baseline experiment and show that combining CC and NC measurements resolves the individual quark couplings, breaking a degeneracy that persists in either analysis alone.