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 ( $v\sin \,(i)=35.1\pm 1.0$ 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 $\mathrm{log}g=4.05\pm 0.17$ . 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.