The Narrow-Field Mode (NFM) on the Multi Unit Spectroscopic Explorer (MUSE) uses laser tomography to correct for atmospheric turbulence at optical wavelengths. Science verification of this new mode of the MUSE instrument took place in September 2018. The science verification observations were obtained in service mode. Out of 37 submitted proposals, 16 observing programmes were scheduled for a total of 43.5 hours of observations. The allocation assumed a seeing better than 0.8 arcseconds, i.e., the required atmospheric conditions to achieve effective adaptive optics correction. Some of the top priority programmes could not be executed because the reference stars were too faint to provide sufficient low-order adaptive optics corrections. As shown by the first results presented here, the NFM will enable advances across a range of scientific areas, for example, characterising substellar/planetary mass objects, globular clusters, and active galactic nuclei.