This paper investigates a distributed optimization problem for high-order strict-feedback nonlinear multiagent systems. A virtual system is built for each agent using a distributed proportional-integral (PI) optimization algorithm to estimate the global optimal solution online. The estimate is then input into a prefilter to generate an alternative estimate and its high-order derivatives. Based on these signals, a backstepping controller is used to make the actual system track the alternative estimate asymptotically, which thereby realizes exact global consensus optimization. Compared to the existing result, the proposed algorithm is fully distributed under undirected topologies with much weaker assumptions on local and global objective functions, lower computation and communication cost. Exact global optimal consensus can also be reached in the cases with directed topologies and intermittent communications. The effectiveness of the method is verified by simulations.