A novel output-feedback controller is proposed for multi-input multi-output (MIMO) nonautonomous nonlinear systems with unstructured uncertainties. The control system under consideration is a non-square MIMO system that may have varying numbers of control inputs and outputs. Apart from the known relative degrees of each output, the system to be controlled is completely unknown and nonautonomous. It is also assumed that the dominant control inputs for a specific system output are unknown. The proposed controller utilizes a higher-order switching differentiator (HOSD) to observe the time derivatives of composite signals that include output tracking errors. This leads to a low-complexity, approximation-free, output-feedback controller capable of compensating for unstructured uncertainties. The controller’s strategy, free from universal approximators, significantly simplifies the control formula and minimizes the number of design constants. The theory shows that all output tracking errors asymptotically converge to zero. The effectiveness of the proposed controller is demonstrated through numerical simulations of three example MIMO systems.