This article addresses event-triggered output-feedback stabilization with a prescribed convergence rate for uncertain nonlinear systems. Typically, the systems allow completely unknown nonlinearities, from which no any information is available for feedback. Nevertheless, an enhanced stabilization objective is pursued in this article to guarantee not only convergence, but particularly prescribed convergence rate. To this end, a distinct event-triggered output-feedback scheme is developed by integrating a powerful compensation technique with the event-triggering mechanism. Specifically, a set of delicate gains, motivated by the funnel control method, are introduced not only to handle the completely unknown nonlinearities and the execution error, but also to guarantee a prescribed rate. Particularly, a new event-triggering mechanism is given, where the threshold and suspension time are online adjusted with respect to the gains. As such, the threshold and suspension time could become adequately small as the gains increase, ensuring timely execution for the effectiveness of the compensation technique. It turns out that the designed event-triggered output-feedback controller guarantees the system states to globally converge to zero with the prescribed convergence rate.