NASA's Transiting Exoplanet Survey Satellite (TESS) mission has been uncovering a growing number of exoplanets orbiting nearby, bright stars. Most exoplanets that have been discovered by TESS orbit narrow-line, slow-rotating stars, facilitating the confirmation and mass determination of these worlds. We present the discovery of a hot Jupiter orbiting a rapidly rotating (vsini=35.1{+/-}1.0km/s) early F3V-dwarf, HD115447 (TOI-778). The transit signal taken from Sectors 10 and 37 of TESS's initial detection of the exoplanet is combined with follow-up ground-based photometry and velocity measurements taken from Minerva-Australis, TRES, CORALIE, and CHIRON to confirm and characterize TOI-778b. A joint analysis of the light curves and the radial velocity measurements yields a mass, a radius, and an orbital period for TOI-778b of 2.76_-0.23_^+0.24^MJup, 1.370{+/-}0.043RJup, and ~4.63days, respectively. The planet orbits a bright (V=9.1mag) F3-dwarf with M=1.40{+/-}0.05M{sun}, R=1.70{+/-}0.05R{sun}, and logg=4.05{+/-}0.17. We observed a spectroscopic transit of TOI-778b, which allowed us to derive a sky-projected spin-orbit angle of 18{+/-}11deg, consistent with an aligned planetary system. This discovery demonstrates the capability of smaller-aperture telescopes such as Minerva-Australis to detect the radial velocity signals produced by planets orbiting broad-line, rapidly rotating stars.