Understanding stable patterns of interpersonal movement coordination is essential to understanding successful social interaction and activity (i.e., joint action). Previous research investigating such coordination has primarily focused on the synchronization of simple rhythmic movements (e.g., finger/forearm oscillations or pendulum swinging). Very few studies, however, have explored the stable patterns of coordination that emerge during task-directed complementary coordination tasks. Thus, the aim of the current study was to investigate and model the behavioral dynamics of a complementary collision-avoidance task. Participant pairs performed a repetitive targeting task in which they moved computer stimuli back and forth between sets of target locations without colliding into each other. The results revealed that pairs quickly converged onto a stable, asymmetric pattern of movement coordination that reflected differential control across participants, with 1 participant adopting a more straight-line movement trajectory between targets, and the other participant adopting a more elliptical trajectory between targets. This asymmetric movement pattern was also characterized by a phase lag between participants and was essential to task success. Coupling directionality analysis and dynamical modeling revealed that this dynamic regime was due to participant-specific differences in the coupling functions that defined the task-dynamics of participant pairs. Collectively, the current findings provide evidence that the dynamical coordination processes previously identified to underlie simple motor synchronization can also support more complex, goal-directed, joint action behavior, and can participate the spontaneous emergence of complementary joint action roles.