(1) Background and objectives: Running-related injuries (RRIs) are commonly attributed to improper running posture and overuse. This study aims to analyze the running motions of individuals with and without RRIs using a sensor-free method, which offers a user-friendly and straightforward approach. (2) Materials and Methods: A total of 155 runners were divided into two groups: the normal runner group (runners who had never been injured, n = 50) and the RRI group (runners who had experience at least one injury while running, n = 105). The forward head posture (FHP), trunk lean, hip rotation, horizontal movement of the center of gravity (COG), vertical movement of the COG, pelvic rotation, hip hike, and type of strike were measured for posture analysis. (3) Results: We found that the left–right balance of the pelvis and the spinal posture during running were associated with RRIs. The difference in hip hike and FHP emerged as key predictors of running-related musculoskeletal injury occurrence from our logistic regression analysis. (4) Conclusions: Identifying pathological movements in runners through running motion analysis without the use of sensors can be instrumental in the prevention and treatment of RRIs.