The ultraviolet (UV) emission from the most numerous stars in the universe, M dwarfs, impacts the formation, chemistry, atmospheric stability, and surface habitability of their planets. We have analyzed the spectral evolution of UV emission from M0-M2.5 (0.3-0.6M{sun}) stars as a function of age, rotation, and Rossby number using Hubble Space Telescope observations of Tucana-Horologium (40Myr), Hyades (650Myr), and field (2-9Gyr) objects. The quiescent surface flux of their CII, CIII, CIV, HeII, NV, SiIII, and SiIV emission lines, formed in the stellar transition region, remains elevated at a constant level for 240{+/-}30Myr before declining by 2.1 orders of magnitude to an age of 10Gyr. The MgII and far-UV pseudocontinuum emission, formed in the stellar chromosphere, exhibits more gradual evolution with age, declining by 1.3 and 1.7 orders of magnitude, respectively. The youngest stars exhibit a scatter of 0.1dex in far-UV line and pseudocontinuum flux attributable only to rotational modulation, long-term activity cycles, or an unknown source of variability. Saturation-decay fits to these data can predict an M0-M2.5 star's quiescent emission in UV lines and the far-UV pseudocontinuum with an accuracy of 0.2-0.3dex, the most accurate means presently available. Predictions of UV emission will be useful for studying exoplanetary atmospheric evolution and the destruction and abiotic production of biologically relevant molecules and interpreting infrared and optical planetary spectra measured with observatories like the James Webb Space Telescope.