Purpose: Acoustic-prosodic entrainment, defined as the tendency for individuals to modify their speech behaviors to more closely align with the behaviors of their conversation partner, plays an important role in successful interaction. From a mechanistic perspective, acoustic-prosodic entrainment is, by its very nature, a rhythmic activity. Accordingly, it is highly plausible that an individual's rhythm perception abilities play a role in their ability to successfully entrain. Here, we examine the impact of rhythm perception in speaking rate entrainment and subsequent conversational quality. Method: A round-robin paradigm was used to collect 90 dialogues from neurotypical adults. Additional assessments determined participants' rhythm perception abilities, social competence, and partner familiarity (i.e., whether the conversation partners knew each other prior to the interaction. Mediation analysis was used to examine the relationships between rhythm perception scores, speaking rate entrainment (using a measure of static local synchrony), and a measure of conversational success (i.e., conversational quality) based on third-party listener observations. Findings were compared to the same analysis with three additional predictive factors: participant gender, partner familiarity, and social competence. Results: Results revealed a relationship between rhythm perception and speaking rate entrainment. In unfamiliar conversation partners, there was a relationship between speaking rate entrainment and conversational quality. The relationships between entrainment and each of the three additional factors (i.e., gender, partner familiarity, and social competence) were nonsignificant. Conclusions: In unfamiliar conversation partners, better rhythm perception abilities were indicative of increased conversational quality mediated by higher levels of speaking rate entrainment. These results support theoretical postulations specifying rhythm perception abilities as a component of acoustic-prosodic entrainment, which, in turn, facilitates conversational success. Knowledge of this relationship contributes to the development of a causal framework for considering a mechanism by which rhythm perception deficits in clinical populations may impact conversational success.