Cantilevers play an important role as linear transducers in nanoscience, with nanomechanical detection of mass and stress as a clear example. We performed gas sensing experiments with a standard functionalized cantilever driven strongly into the regime of nonlinear oscillations. We compared the cantilever response to the selective adsorption of ethanol vapour in the nonlinear regime, to the ones obtained in the conventional linear static and dynamic sensing modes. In the nonlinearly driven cantilever, the adsorption and desorption-induced frequency shifts were enhanced by over a factor of three compared to resonant sensing with the same mode in the linear regime. This demonstrates a route towards gas detectors that exploit nonlinearity to enhance the responsivity, which can be implemented with standard cantilever devices.