Cellular vehicle-to-everything (C-V2X) is a communication technology that supports various safety, mobility, and environmental applications, given its higher reliability properties compared to other communication technologies. The performance of these C-V2X-enabled intelligent transportation system (ITS) applications is affected by the performance of the C-V2X communication technology (mainly packet loss). Similarly, the performance of the C-V2X communication is dependent on the vehicular traffic density which is affected by the traffic mobility patterns and vehicle routing strategies. Consequently, it is critical to develop a tool that can simulate, analyze, and evaluate the mutual interactions of the transportation and communication systems at the application level to quantify the benefits of C-V2X-enabled ITS applications realistically. In this paper, we demonstrate the benefits gained when using C-V2X Vehicle-to-Infrastructure (V2I) communication technology in an energy-efficient dynamic routing application. Specifically, we develop a Connected Energy-Efficient Dynamic Routing (C-EEDR) application using C-V2X as a communication medium in an integrated vehicular traffic and communication simulator (INTEGRATION). The results demonstrate that the C-EEDR application achieves fuel savings of up to 16.6% and 14.7% in the IDEAL and C-V2X communication cases, respectively, for a peak hour demand on the downtown Los Angeles network considering a 50% level of market penetration of connected vehicles. The results demonstrate that the fuel savings increase with increasing levels of market penetration at lower traffic demand levels (25% and 50% the peak demand). At higher traffic demand levels (75% and 100%), the fuel savings increase with increasing levels of market penetration with maximum benefits at a 50% market penetration rate. Although the communication system is affected by the high density of vehicles at the high traffic demand levels (75% and 100% the peak demand), the C-EEDR application manages to perform reliably, producing system-wide fuel consumption savings.The C-EEDR application achieves fuel savings of 15.2% and 11.7% for the IDEAL communication and 14% and 9% for the C-V2X communication at the 75% and 100% market penetration rates, respectively. Finally, the paper demonstrates that the C-V2X communication constraints only affect the performance of the C-EEDR application at the full demand level when the market penetration of the connected vehicles exceeds 25%. This degradation, however, is minimal (less than a 2.5% reduction in fuel savings).