As an essential household economic factor, household savings with increasing income affect household energy access. However, there is limited understanding of the household savings accumulation differs the impact of income on household energy and related CO₂. Based on the panel data of 284 cities in China, a threshold regression model is constructed to investigate the non-linear effects of income on urban household carbon emissions at different saving levels. We found that the heterogeneity of residential savings substantially mattered the income effect on urban household carbon emission. Especially, low-saving households struggled to obtain clean energy, needed more government intervention to replace the fossil fuel system with a clean household energy system. By comparison, middle- and high-saving households could easily transit towards a clean energy system, including natural gas and electricity. Moreover, residential income strongly drives the rising household electricity and related CO₂ at the upper-middle saving level. High-saving households showed high sensitivity to heating energy in northern China. In addition, an in-depth analysis of challenges faced by the energy consumption of Chinese urban households in coping with climate change is carried out, and policy recommendations in most undeveloped regions of China and other counties with high-carbon energy structures are put forward accordingly.