The spatial autocorrelation analysis method was applied to panel data from the provinces of China (including autonomous regions and municipalities directly under the central government) for the period 2003 to 2016 in order to construct a spatial Durbin model of technological progress and financial support in relation to reductions in carbon emissions. The results show that China’s carbon intensity presents significant spatial spillover effects under different spatial weights, which indicates that the carbon intensity of a province is influenced not only by its own characteristics, but also by the carbon emission behaviors of geographically adjacent and economically similar provinces and regions. Financial structure, financial scale, and financial efficiency all have significant effects on carbon intensity within a province, while financial structure is also linked to carbon intensity in other regions, but financial scale has no significant spillover effect on carbon intensity in space. Areas with high financial efficiency can reduce their own carbon intensity as well as that of surrounding areas. The inter-regional spillover effect of technological progress on carbon intensity is stronger than the spillover effect, but there is a time lag.