The quantum-classical path integral (QCPI) provides a rigorous methodology for simulating condensed phase processes when a fully quantum mechanical description of a small subsystem is necessary. While full QCPI calculations have been shown to be feasible on parallel computing platforms, the large number of trajectory calculations required leads to computational cost that significantly exceeds that of classical molecular dynamics calculations. This paper describes the harmonic back-reaction (HBR) approximation to the QCPI expression, which reduces dramatically the computational cost by requiring a single classical trajectory from each initial condition. Test calculations on a model of strongly anharmonic oscillators show that the HBR treatment quantitatively reproduces the full QCPI results. The HBR-QCPI algorithm is applicable to a variety of condensed phase and biological systems with effort only somewhat greater than that of molecular dynamics simulations.