This paper addresses the re-engineering of congestion control for TCP applications over networks with coupled wireless links. Using queueing delay as a congestion measure, we show that optimal TCP congestion control can be achieved by developing window-control oriented implicit primal-dual solvers for intended network utility maximization problem. Capitalizing on such an idea, we prove the existence of scalable, easy-to-deploy, yet optimal end-to-end congestion control schemes for networks with wireless links, given that the wireless access point appropriately schedules packet transmissions. A class of so-called QUIC-TCP congestion control algorithms are developed. Relying on a Lyapunov method, we rigorously establish the global convergence/stability of the proposed QUIC-TCP to optimal equilibrium in the network fluid model. Numerical results corroborate the merits of the proposed schemes in IPv6-based Internet environments. INDEX TERMS Congestion control, wireless-link scheduling, convex optimization, network fluid model, Lyapunov method.