This paper is dealt with the problem of prescribed performance control (PPC) for the strict-feedback systems with piecewise continuous references. The discontinuity of the reference results in the abrupt variations of the tracking error and the intermediate errors, which renders the existing PPC designs challenging. To overcome this difficulty, a tuning function-based approach to adapting the performance funnels is proposed. In this way, the performance functions are reasonably modified in accordance with the discontinuity of the errors, such that all the errors converge to the predefined bounds in the given time after the discontinuity occurs. Moreover, this approach is compatible with the standard PPC method in the sense that it preserves the inherent robustness of PPC against the model uncertainties of the system. Despite unknown nonlinearities, there is no need to employ neural networks or fuzzy logic systems for approximation. The simulation results on a single-link robotic manipulator illustrate the theoretical findings.