R&D investment plays a great role in achieving China’s low-carbon economy goals, which has a moderating effect on the relationship between income and carbon emissions. Furthermore, such a moderating effect may have spatial differences, given the possible spatial dependence of carbon emissions. Therefore, this paper explores the direct and spatial spillover moderating effects of R&D investment by adopting the panel spatial Durbin model and data of 30 provinces in China during 1998–2015. The empirical results firstly indicate that R&D investment moderates the positive impact of income on local carbon emissions for both the non-spatial and spatial model, and that more R&D investment can make carbon emissions reach the turning point earlier. Secondly, R&D investment in the local province increases the positive influence of local income on neighboring carbon emissions, which mainly results from the transfer effect of carbon emissions rather than the knowledge spillovers effect. The results are indicated to be robust by three types of robustness analyses. Finally, FDI and patents are the main constrained forces of local and neighboring carbon emissions; coal consumption is the main driver of local carbon emissions.