The current digitalization trend, the increased attention towards sustainability, and the spread of the business analytics call for higher efficiency in port operations and for investigating the quantitative approaches for maritime logistics and freight transport systems. Thus, this manuscript aims at enabling analytics-driven improvements in the port transportation processes efficiency by streamlining the related information flow, i.e., by attaining shorter time frames of the information and document sharing among the export stakeholders. We developed a case study in a mid-sized European port, in which we applied Process Mining (PM)—an emerging type of business analytics—to a seven-month dataset from the freight export process. Four process inefficiencies and an issue that can jeopardize the reliability of the time performance measurements were detected, and we proposed a draft of solutions to cope with them. PM enabled enhancements in the overall export time length, which might improve the vessels’ turnover and reduce the corresponding operational costs, and supported the potential re-design of performance indicators in process control and monitoring. The results answer the above-mentioned calls and they offer a valuable, analytics-based alternative to the extant approaches for improving port performance, because it focuses on the port information flow, which is often related to sustainability issues, rather than the physical one.