This paper solves the problem of projective lag‐synchronization based on output‐feedback control for chaotic drive‐response systems with input dead‐zone and sector nonlinearities. This class of the drive‐response systems is assumed in Brunovsky form but with unavailable states and unknown dynamics. To effectively deal with both dead‐zone and sector nonlinearities, the proposed controller is designed in a variable‐structure framework. To online learn the uncertain dynamics, adaptive fuzzy systems are used. And to estimate the unavailable states, a simple synchronization error is constructed. To prove the stability of the overall closed‐loop system (controller, observer, and drive‐response system) and to design the adaptation laws, a Lyapunov theory and strictly positive real (SPR) approach are exploited. Finally, three academic examples are given to show the effectiveness of this proposed lag‐synchronization scheme.