The synchronization problem of complex dynamical networks (CDNs) with nonlinearities, uncertainties, time-varying input delays and disturbances is investigated in this article. The key objective of this work is to estimate both the matched and mismatched disturbance signals, which is accomplished by making use of improved-equivalent-input-disturbance estimator (IEIDE) technique. Subsequently, the impact of time-delays in control input can be effectively handled by means of extended Smith predictor (ESP) approach. To be precise, an unified dynamic output feedback control protocol is developed for dealing the disturbances and input delays by combining IEIDE and ESP strategy for nonlinear CDNs. Moreover, Lyapunov stability theory is utilized for the resultant closed-loop system to deduce the linear matrix inequality (LMI)-based sufficient stability conditions, which ensure the asymptotic synchronization of the considered system. In addition, the unpredictable disturbance signals are estimated with high precision based on the proposed control design. More precisely, the desired gain matrices are obtained by solving the LMI-based conditions. In the final analysis, the simulation results of the Lur'e system are provided to examine the practicability and efficacy of the developed control strategy.