http://scienceblogs.com/grrlscientist/2010/04/the_kalahari_persistence_hunt.php

By all accounts humans have done this, in various forms, for thousands of years. American indians were recorded as using a variation that used a relay of hunters. By careful observation it was known which way the game would run. Which makes it possible to pre-position hunters along the route. With the deer getting weaker by the minute and hunters running at top speed but being replaced one after another the pursuit was quickly over.

Using a spear to dispatch prey is efficient and wise. Even an exhausted deer might muster a kick that could do serious damage. But I have read that hunters commonly used a knife or kept rousing the animal until it fell over dead.