The ultraviolet-visible wavelength range holds critical spectral diagnostics for the chemistry and physics at work in planetary atmospheres. To date, time-series studies of exoplanets to characterize their atmospheres have relied on several combinations of modes on the Hubble Space Telescope's STIS/COS instruments to access this wavelength regime. Here for the first time, we apply the Hubble WFC3/UVIS G280 grism mode to obtain exoplanet spectroscopy from 200 to 800 nm in a single observation. We test the G280 grism mode on the hot Jupiter HAT-P-41b over two consecutive transits to determine its viability for the characterization of exoplanet atmospheres. We obtain a broadband transit depth precision of 29-33 ppm and a precision of on average 200 ppm in 10 nm spectroscopic bins. Spectral information from the G280 grism can be extracted from both the positive and negative first-order spectra, resulting in a 60% increase in the measurable flux. Additionally, the first Hubble Space Telescope orbit can be fully utilized in the time-series analysis. We present detailed extraction and reduction methods for use by future investigations with this mode, testing multiple techniques. We find the results to be fully consistent with STIS measurements of HAT-P-41b from 310 to 800 nm, with the G280 results representing a more observationally efficient and precise spectrum. HAT-P-41b's transmission spectrum is best fit with a model with Teq = 2091 K, high metallicity, and significant scattering and cloud opacity. With these first-of-their-kind observations, we demonstrate that WFC3/UVIS G280 is a powerful new tool to obtain UV-optical spectra of exoplanet atmospheres, adding to the UV legacy of Hubble and complementing future observations with the James Webb Space Telescope.