In this article, a novel Lyapunov-based approach for strong prescribed-time stabilization by periodic delayed feedback is established. Since the comparison lemma cannot be directly applied to time-delay systems, their proofs rely on trajectory analysis. Based on this approach, a novel control law for strong prescribed-time stabilization of uncertain scalar nonlinear systems is obtained, with the following appealing properties: singularity problems inherent to time-varying high gain approaches are avoided; strong prescribed-time stabilization is achieved with control terms exhibiting a linear growth rate in the combined current and delayed state variable; the achieved fixed-time stability is preserved under classes of additive perturbations; and the setting time of the closed-loop system equals the prescribed value for some admissible uncertainties. Subsequently, using the backstepping procedure, a strongly prescribed-time stabilizing control law for strict feedback uncertain nonlinear systems is designed. Numerical simulations are shown to verify the effectiveness of the proposed approaches.