Asynchronous online discussions (AODs) are increasingly prevalent in higher education to adapt to educational changes and promote critical thinking among learners. Past research has emphasized instructors' facilitation roles in encouraging learners' critical thinking in AODs, while fewer studies explored peer facilitation and peer participants' critical thinking from the students' perspective as facilitators. This study used a lag sequential analysis approach to examine peer facilitation techniques and critical thinking in a peer-facilitated AOD spanning six tasks over 12 weeks with 40 undergraduate participants. Results highlighted that the most frequently used peer facilitation techniques were "giving own opinions or experiences" and "questioning," with the latter demonstrating the highest number of significant sequential patterns. Peer participants' critical thinking primarily involved "analyse" and "evaluate," with significant sequential patterns observed in lower level and higher order critical thinking stages but not between them. Further investigation revealed the impact of peer facilitation techniques on critical thinking, and a new three-phase model was developed to describe their associations. These findings suggest that dynamic peer facilitation techniques effectively enhance critical thinking, with specific techniques targeting distinct phases of its development in AODs. The study provides actionable insights for educators, offering strategies to optimize facilitation approaches and foster critical thinking skills in higher education settings.