Abstract We explore the role of matter effect in the evolution of neutrino oscillation parameters in the presence of lepton-flavor-conserving and lepton-flavor-violating neutral-current non-standard interactions (NSI) of the neutrino. We derive simple approximate analytical expressions showing the evolution of mass-mixing parameters in matter with energy in the presence of standard interactions (SI) and SI+NSI (considering both positive and negative values of real NSI parameters). We observe that only the NSI parameters in the (2,3) block, namely εμτ and (γ − β) ≡ (εττ− εμμ) affect the modification of θ23. Though all the NSI parameters influence the evolution of θ13, εeμ and εeτ show a stronger impact at the energies relevant for DUNE. The solar mixing angle θ12 quickly approaches to ∼ 90° with increasing energy in both SI and SI+NSI cases. The change in ∆$$ {m}_{21,m}^2 $$ m 21 , m 2 is quite significant as compared to ∆$$ {m}_{31,m}^2 $$ m 31 , m 2 both in SI and SI+NSI frameworks for the energies relevant for DUNE baseline. Flipping the signs of the NSI parameters alters the way in which mass-mixing parameters run with energy. We demonstrate the utility of our approach in addressing several important features related to neutrino oscillation such as: a) unraveling interesting degeneracies between θ23 and NSI parameters, b) estimating the resonance energy in presence of NSI when θ13 in matter becomes maximal, c) figuring out the required baselines and energies to have maximal matter effect in νμ → νe transition in the presence of different NSI parameters, and d) studying the impact of NSI parameters εμτ and (γ − β) on the νμ → νμ survival probability.