The service and knowledge economy has emerged as the primary drivers of national economic growth, with the tertiary industry leading the way. To promote growth in the central plain region and achieve structural convergence of industries for sustainable, rapid, and healthy economic development, conducting a spatial structural analysis of the evolution of the industrial structure is essential. However, traditional statistical analysis needs to keep pace with the dynamic and non-linear relationships within and outside industries. In this paper, we propose a novel spatial analysis method based on the gravity model to examine the tertiary industry in China’s central plains economic region (CPER). By analyzing statistical data from 2018 to 2022, our results reveal that the economic linkage intensity (F-value) of the tertiary industry in CPER has increased over the years. Specifically, F-values for the high-end, general, and other service industries are 2815, 9882, and 14,826, respectively. The network density (D-value) indicates a single-core structure, with D-values of 0.71, 0.74, and 0.82 for high-end, general, and other service industries. Our findings suggest that the economic linkage network of the tertiary industry in CPER has matured, with solid industry integration and convergence of the regional financial industry structure. There is a high correlation (p < 0.01) among various network structures in the service industry, and a stable and cohesive subgroup with multicentre characteristics is beginning to emerge. These findings provide valuable insights for the development of the tertiary industry in CPER during the later stage of the 14th Five-Year Plan in China.