This study uses a maze navigation task in conjunction with a quasi-scripted, prosodically controlled speech task to examine acoustic and articulatory accommodation in pairs of interacting speakers. The experiment uses a dual electromagnetic articulography set-up to collect synchronized acoustic and articulatory kinematic data from two facing speakers simultaneously. We measure the members of a dyad individually before they interact, while they are interacting in a cooperative task, and again individually after they interact. The design is ideally suited to measure speech convergence, divergence, and persistence effects during and after speaker interaction. This study specifically examines how convergence and divergence effects during a dyadic interaction may be related to prosodically salient positions, such as preceding a phrase boundary. The findings of accommodation in fine-grained prosodic measures illuminate our understanding of how the realization of linguistic phrasal structure is coordinated across interacting speakers. Our findings on individual speaker variability and the time course of accommodation provide novel evidence for accommodation at the level of cognitively specified motor control of individual articulatory gestures. Taken together, these results have implications for understanding the cognitive control of interactional behavior in spoken language communication.