It is important to explore the energy–economy–environment (3E) coupling mechanism for building a sustainable economy in the context of carbon-peaking and carbon-neutralization strategy. Based on the DPSIRM (driving force–pressure–state–influence–response–management) theoretical model, this paper constructs the evaluation system of 3E coupling-coordinated development, takes the carbon-neutral and sustainable-development strategy and spatiotemporal heterogeneity into account in the index system, and constitutes the energy–economy–environment and carbon-neutral strategy–sustainable development–space (3E3S) strategic-development model. This paper uses the coupling-coordination-degree model to measure the coordinated development of 3E in Jiangsu from 2010 to 2020 and analyzes the time-sequence evolution and spatial-difference evolution characteristics of the coupling-coordinated development. The results show that (1) when the coupling coefficient of 3E was in a stable and high-level coupling state and the correlation degree of each system was high, the coupling-coordination degree increased from 0.4 in 2010 to 0.7 in 2020; the level of coordination of 3E coupling transited from the initial maladjustment recession to the intermediate coordinated development and moved towards high-quality coordinated development. (2) In addition, at the beginning, the development level of southern and central Jiangsu was generally higher than that of northern Jiangsu; in the middle term, the overall development was in a stage of barely coordinated development. The urban difference between northern and central Jiangsu was relatively high, and the level in southern Jiangsu was generally high; in the later stage, the overall development was in a well-coordinated stage. The development of southern Jiangsu was relatively saturated, gradually approaching the stage of high-quality coordinated development. Roughly speaking, in 2010, the average level of coupling coordination degree of South Jiangsu, Central Jiangsu, and North Jiangsu was 0.5, 0.4, and 0.3, respectively; by 2020, it had developed to 0.9, 0.8, and 0.7, respectively, and the development level rose steadily despite regional differences. The level of coupling coordination generally increased from north to south. Therefore, strengthening the strategic-development awareness of 3E and establishing and improving the government consultation mechanism according to local conditions will help decision-makers to formulate effective regional sustainable-development and carbon-neutral strategies and form a coordinated-development strategy of 3E3S in Jiangsu.