Despite a surge of interest in the nonlinear transport in 2D materials, a fundamental puzzle remains: existing theoretical frameworks are unable to quantitatively account for the giant nonlinear conductivities (≳ 1 (μ m)/(Ω V)) recently reported in 2D van der Waals heterostructures. Here, we introduce a mechanism based on electron scattering from a substrate-induced dipole array linked to short-range impurities. We show that the strict kinematic constraints, inherent to 2D scattering, lead to a singular enhancement of the nonlinear response, fundamentally dictating a natural scale of 1 (μ m)/(Ω V).