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 ( v sin ( i ) = 35.1 ± 1.0 km s−1) early F3V-dwarf, HD 115447 (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-778 b. A joint analysis of the light curves and the radial velocity measurements yields a mass, a radius, and an orbital period for TOI-778 b of 2.76 − 0.23 + 0.24 M J, 1.370 ± 0.043 R J, and ∼4.63 days, respectively. The planet orbits a bright (V = 9.1 mag) F3-dwarf with M = 1.40 ± 0.05 M ⊙, R = 1.70 ± 0.05 R ⊙, and log g = 4.05 ± 0.17 . We observed a spectroscopic transit of TOI-778 b, which allowed us to derive a sky-projected spin-orbit angle of 18° ± 11°, 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.