Urbanization becomes the primary source of carbon emissions and energy demand growth in China with industrialization entering the middle-later stages. With the current high-consumption and high-emission urban development model, the resulting resource consumption and carbon emissions become a major environmental issue and a sustainability problem. Based on the panel data of the bay area economic zone of Zhejiang province from 2003 to 2017, this paper analyzed the overall spatial and temporal distribution characteristics of carbon emissions of the economic zone. The main sources of carbon emissions will be studied in detail by incorporating the urbanization level, energy consumption structure, land use, economic development level, industrial structure, population agglomeration, openness, and technological progress into the STIRPAT (the Stochastic Impacts by Regression on Population, Affluence, and Technology) extended model. We further investigated the driving mechanism of carbon emissions and spatial and temporal heterogeneity of carbon emissions from the perspective of urbanization using the geographically and temporally weighted regression (GTWR). The results showed that: (1) The scale of carbon emissions has increased with time, but the growth rate has not been large with a decreasing growth rate. Carbon emissions in different regions are significantly different. The carbon emission is less intense through the years with a spatial distribution pattern of increasing from the southwest to the northeast. (2) The level of economic development and the degree of openness to the outside world are the dominant factors that affect the carbon emission level, followed by energy consumption structure, technological progress, and urbanization. (3) These influencing factors show substantial spatiotemporal heterogeneity that the direction and intensity of the fluctuations of various driving factors vary from time to time and region to region. This paper analyzed the impact of the driving factors of carbon emissions in the economic zone of Zhejiang Bay Area explicitly, providing scientific support for the implementation of regionally differentiated carbon emission reduction strategies. It is necessary to fully examine the actual development of each region to formulate a differentiated carbon emission reduction regulation strategy. In particular, these measures should be taken into consideration for reducing carbon emissions in the area: enhancing the efficiency of comprehensive utilization of resources by accelerating the construction of science and technology innovation corridors, and promoting the transformation and upgrading of traditional industries by fully introducing modern service industries and high-end manufacturing based on information technology.