This paper studies the impact of integrating pricing with connection admission control (CAC) on the congestion management practices in contention-based wireless random access networks. Notably, when the network is free of charge, each self-interested user tries to occupy the channel as much as possible, resulting in the inefficient utilization of network resources. Pricing is therefore adopted as incentive mechanism to encourage users to choose their access probabilities considering the real-time network congestion level. A Stackelberg leader-follower game is formulated to analyze the competitive interaction between the service provider and the users. In particular, each user chooses the access probability that optimizes its payoff, while the self-interested service provider decides whether to admit or to reject the user's connection request in order to optimize its revenue. The stability of the Stackelberg leader-follower game in terms of convergence to the Nash equilibrium is established. The proposed CAC scheme is completely distributed and can be implemented by individual access points using only local information. Compared to the existing schemes, the proposed scheme achieves higher revenue gain, higher user payoff, and higher QoS performance.