A finite-time extended, state-observer-based, fixed-time backstepping control algorithm was designed for hypersonic flight vehicles. To enhance the robustness of the controller, two novel finite-time extended state observers were introduced to compensate for the negative effects of lumped disturbances such as uncertainties and external disturbances. Two hyperbolic sine tracking differentiators were used to approximate the derivatives of the virtual control signals and guidance commands, thereby alleviating the computational burden associated with traditional backstepping control. Furthermore, a fixed-time backstepping attitude controller was used to guarantee that the tracking errors converged to a small neighbor of the origin in fixed time. According to the simulation results, the proposed controller outperformed a fixed-time sliding mode disturbance, observer-based, finite-time backstepping controller in terms of the tracking precision and convergence rate. Moreover, the proposed controller was noted to be robust in simulations involving lumped disturbances.