Entanglement is closely related to some fundamental features of the dynamics of composite quantum systems: quantum entanglement enhances the" speed" of evolution of certain quantum states, as measured by the time required to reach an orthogonal state. The concept of" speed" of quantum evolution constitutes an important ingredient in any attempt to determine the fundamental limits that basic physical laws impose on how fast a physical system can process or transmit information. Here we explore the relationship between entanglement and the speed of quantum evolution in the context of the quantum brachistochrone problem. Given an initial and a final state of a composite system we consider the amount of entanglement associated with the brachistochrone evolution between those states, showing that entanglement is an essential resource to achieve the alluded time-optimal quantum evolution.