Revealing how historical energy and environmental policies interacted with socioeconomic factors to shape the trends in air pollutant and CO2 emissions is crucial for developing effective future pollution-carbon co-control strategies. Here, we develop an integrated analytical framework combining a detailed sectoral emission inventory, index decomposition analysis, and a clustering algorithm to investigate China's synergetic patterns of air pollutant and CO2 emissions across 15 socioeconomic sectors from 2000 to 2020 and uncover the co-drivers behind these trends, with detailed temporal, sectoral, and spatial dynamics revealed. Our analysis suggests that historical policies have effectively curbed air pollutant emissions, while abating CO2 emissions remains a challenge. Energy and climate policies, particularly those focused on structural adjustments, are increasingly instrumental in driving pollution-carbon co-reduction. Compared to the earlier period, the fractional contribution of energy and climate policies to emission reductions of SO2, NOx, PM2.5, and CO2 increased by 1.3-8.6 times during 2010-2020, respectively. Substantial regional heterogeneity in emission co-drivers underscores the need for tailored strategies, such as adopting advanced energy-saving technologies in areas dominated by energy-intensive industries and accelerating the clean energy transition in regions endowed with renewable resources. Our study would provide actionable insights for formulating effective pollution-carbon co-control strategies in China and beyond.