Let F_n(Σ_g,1) denote the configuration space of n ordered points on the surface Σ_g,1 and let Γ_g,1 denote the mapping class group of Σ_g,1. We prove that the action of Γ_g,1 on H_i(F_n(Σ_g,1); ℤ) is trivial when restricted to the ith stage of the Johnson filtration J(i) ⊂ Γ_g,1. We give examples showing that J(2) acts nontrivially on H₃(F₃(Σ_g,1)) for g ≥ 2, and provide two new conceptual reinterpretations of a certain group introduced by Moriyama.