This paper presents an output feedback indirect dynamic inversion (IDI) approach for a class of uncertain nonaffine systems with input unmodelled dynamics. Compared with previous approaches to achieve performance recovery, the proposed method aims at dealing with a broader class of nonaffine-in-control systems with triangular structure. An IDI state feedback law is designed first, in which less knowledge of the model plant is needed compared to earlier approximate dynamic inversion methods, thus yielding more robust performance. After that, an extended high-gain observer is designed to accomplish the task with output feedback. Finally, we prove that the designed IDI controller is equivalent to an adaptive proportional-integral (PI) controller, with respect to both time response equivalence and robustness equivalence. The conclusion implies that for the studied strict-feedback non-affine systems with unmodelled dynamics, there always exits a PI controller to stabilise the systems. The effectiveness and benefits of the designed approach are verified by three examples.