GRB 130427A occurred in a relatively nearby galaxy; its prompt emission had the largest GRB fluence ever recorded. The afterglow of GRB 130427A was bright enough for the Nuclear Spectroscopic Telescope ARray (NuSTAR) to observe it in the 3-79 keV energy range long after its prompt emission (similar to 1.5 and 5 days). This range, where afterglow observations were previously not possible, bridges an important spectral gap. Combined with Swift, Fermi, and ground-based optical data, NuSTAR observations unambiguously establish a single afterglow spectral component from optical to multi-GeV energies a day after the event, which is almost certainly synchrotron radiation. Such an origin of the late-time Fermi/Large Area Telescope >10 GeV photons requires revisions in our understanding of collisionless relativistic shock physics.