In this paper, the authors consider the problem of tyre blowout control via output feedback for an electric vehicle (EV) driven by four in-wheel motors to reduce fatal damage. First, an EV dynamic model in the case of a tyre blowout is established. The model considers the unmeasurable state, unknown added front wheel steering angle generated by a tyre blowout and uncertain external disturbances. Second, to address the difficulties in estimating the unmeasurable state, unknown parameters and disturbances for the EV, a finite-time observer is introduced. Then, by introducing a coordinate transformation, the state-space model of an EV with tyre blowout is converted into a simple form for which a state feedback control law is constructed by adding a power integrator method. Combining the finite-time observer with the finite-time control law, an output feedback controller is designed to stabilize the EV when a tyre bursts. A torque allocation method is also given to operate every wheel except the burst tyre to stabilize and stop the EV. Finally, computer simulations are given to validate the proposed finite-time output feedback controller for the EV tyre blowout control.