This paper investigates the existing and missing connections between the concepts of project management success and organizational success. We build a theoretical framework of the concepts and elaborate on it by examining three innovation project cases—a smart-city project with little organizational success-driven performance measurement, a product development project with overly ambitious project management goals but an overall positive organizational impact, and an R&D project involving practically no project management performance measurement since organizational success was considered paramount. Our unit of analysis in these cases is performance measurement in terms of its alignment or misalignment of success. We contribute to the literature by (1) examining the linkage between organizational success and project performance criteria, (2) exhibiting the interrelations, dominance, and use of certain project performance measures in determining whether a project is successful, and (3) offering a framework for understanding how performance measurement can support success in project-based operations.