In bipartite consensus tracking (BCT) tasks for nonlinear multiagent systems (MASs), stochastic disturbances and actuator faults are regarded as essential factors that hamper effective controller formulation and tracking precision improvement. To address these difficulties, we design an improved finite-time performance function (FTPF) for a fuzzy fault-tolerant distributed cooperative control scheme to achieve finite-time robust precision BCT tasks for nonlinear MASs. The parameter selection range of the improved FTPF is relaxed, which renders systems to achieve better transient performance. Benefitting from the stochastic Lyapunov stability theory, it is shown that all signals of systems are semiglobal uniformly ultimately bounded in probability, and bipartite consensus errors can satisfy the arbitrary precision with probability in the predefined time. Finally, to verify its effectiveness, the proposed control scheme is applied to BCT tasks of a group of vehicles, which manifests anticipated control performance under various uncertainties.