Overkill by human hunting has been cited consistently as a likely cause of the Pleistocene megafaunal extinctions in Australia, but little archaeological evidence has been found to support the notion of prehistoric Aboriginal people engaging in specialised “big game” hunting more than 40 millennia ago. Here we develop a demographic population model that considers explicitly the potential impact of harvest of small, immature (and presumably more vulnerable) individuals of the largest known marsupial, Diprotodon optatum. We show that remarkably low levels of exploitation of juveniles (the equivalent of one or two kills per 10 people per year) would have been sufficient to drive these large species to extinction within centuries, as a consequence of their “slow” life-histories. This conclusion is robust to assumptions regarding the compensatory response of the prey species and declines in the relative efficiency of hunting as the megafaunal populations declined. These findings dispel the idea that, at least in Australia, evidence for a sophisticated hunting toolkit and massive kill-sites are a necessary adjunct to “blitzkrieg”. Ironically, although the extinction event was likely geochronologically instantaneous (given the coarse resolution of dating from that time), on the scale of human (and megafaunal) lifetimes, the unfolding overkill would have been all but imperceptible.