The destruction of vegetation structure and quantity leads to the weakening of the carbon sequestration capacity of the ecosystem. Building an ecological spatial network is a potent method for studying vegetation spatial distribution structures. The relationship between the spatial distribution structure of vegetation networks and carbon sequestration, as approached from the perspective of complex network theory, is understudied. This study uses the minimum resistance model (MCR) and morphological spatial pattern analysis (MSPA) to study the eco-space network and ecological node spatial structure and topological characteristics of vegetation in the ecologically sensitive area of the middle reaches of the Yellow River (ESAMRYR). Based on the Carnegie-Ames-Stanford approach (CASA) model, the vegetation Net Primary Productivity (NPP) of the study area is calculated, and the ecological carbon sequestration function of the ecological node is estimated, and the relationship between the ecological node and the topological indicators is analyzed. The study shows that the forest land carbon storage in the regions situated toward the south and east of the Yellow River ecologically sensitive area is the highest, accounting for twice the proportion of the area, and is very important in terms of increasing carbon storage. Most of the ecological sources in the study area have a higher topological importance than functional importance, and the sources with low coordination are mainly distributed in the southwest and northeast. We construct a topology and function coupling optimization model (TFCO) to explore the coordination between vegetation structure and carbon sequestration function, to determine the network optimization direction, and to propose optimization solutions. Analysis of network robustness and carbon sequestration capacity shows that the sturdiness and carbon sequestration of the enhanced network are significantly improved. This study provides strategies and methods for protecting ecological sensitive areas, optimizing vegetation spatial distribution, and enhancing carbon sequestration capacity.