“Common prosperity depends on development, and development comes first in transportation.” Achieving common prosperity is the essential requirement for Chinese-style modernization under the construction of a sustainable transportation power country. Based on China’s 30 provincial panel data from 2001 to 2021, this paper calculates the common prosperity index under modernization construction and uses the fixed-effect model and bootstrap mediation effect analysis method to examine the impact and promotion path of transportation infrastructure empowering common prosperity (mediating effect). The study found that transportation infrastructure has a significant enabling effect on common prosperity, and the higher the level of common prosperity, the stronger this effect. After a variety of robustness tests, the conclusion is still reliable. The specific path is that transportation infrastructure further strengthens its role in empowering common prosperity through the four intermediaries of economic growth, factor flow, industrial upgrading, and market expansion. Except for the complete intermediary effect of factor flow, the other intensity ratios are all at 65% or above. In addition, there is heterogeneity in the impact of transportation infrastructure on common prosperity, which is reflected in the significant effect in areas with large urban populations, eastern regions, and first-tier or former new first-tier cities. To this end, a quadrilateral orientation focusing on “economy, factors, industries, and markets” is proposed, with dense transportation networks and regional differentiation as the focus of sustainable transportation development, providing empirical support for promoting common prosperity.