The Beijing-Tianjin-Hebei (BTH) region has been suffering from the most severe fine particle (PM_2.5) pollution in China, which causes serious health damage and economic loss. Quantifying the source contributions to PM_2.5 concentrations has been a challenging task because of the complicated non-linear relationships between PM_2.5 concentrations and emissions of multiple pollutants from multiple spatial regions and economic sectors. In this study, we use the Extended Response Surface Modeling (ERSM) technique to investigate the nonlinear response of PM_2.5 and its major chemical components to emissions of multiple pollutants from different regions and sectors over the BTH region, based on over 1000 simulations by a chemical transport model (CTM). The ERSM-predicted PM_2.5 concentrations agree well with independent CTM simulations, with correlation coefficients larger than 0.99 and mean normalized errors less than 1&amp;thinsp;%. Using the ERSM technique, we find that primary inorganic PM_2.5 is the single pollutant which makes the largest contribution (24&amp;ndash;36&amp;thinsp;%) to PM_2.5 concentrations. The contribution of primary inorganic PM_2.5 emissions is especially high in heavily polluted winter, and is dominated by the industry as well as residential and commercial sectors, which should be prioritized in PM_2.5 control strategies. The total contributions of all precursors (nitrogen oxides, NO_<i>x</i>; sulfur dioxides, SO₂; ammonia, NH₃; non-methane volatile organic compounds, NMVOC; intermediate-volatility organic compounds, IVOC; primary organic aerosol, POA) to PM_2.5 concentrations range between 31&amp;thinsp;% and 48&amp;thinsp;%. Among these precursors, PM_2.5 concentrations are primarily sensitive to the emissions of NH₃, NMVOC&amp;thinsp;+&amp;thinsp;IVOC, and POA. The sensitivities increase substantially for NH₃ and NO_<i>x</i>, and decrease slightly for POA and NMVOC&amp;thinsp;+&amp;thinsp;IVOC with the increase in the emission reduction ratio, which illustrates the nonlinear relationships between precursor emissions and PM_2.5 concentrations. The contributions of primary inorganic PM_2.5 emissions to PM_2.5 concentrations are dominated by local emission sources, which account for over 75&amp;thinsp;% of the total primary inorganic PM_2.5 contributions. For precursors, however, emissions from other regions could play similar roles as local emission sources in the summer and over the northern part of BTH. The source contribution features for various types of heavy-pollution episodes are distinctly different from each other, and from the monthly mean results, illustrating the need of discrepant temporary control strategies for different pollution types.