The fastest and most manoeuvrable terrestrial animals are found in savannah habitats, where predators chase and capture running prey. Hunt outcome and success rate are critical to survival, so both predator and prey should evolve to be faster and/or more manoeuvrable. Here we compare locomotor characteristics in two pursuit predator-prey pairs, lion-zebra and cheetah-impala, in their natural savannah habitat in Botswana. We show that although cheetahs and impalas were universally more athletic than lions and zebras in terms of speed, acceleration and turning, within each predator-prey pair, the predators had 20% higher muscle fibre power than prey, 37% greater acceleration and 72% greater deceleration capacity than their prey. We simulated hunt dynamics with these data and showed that hunts at lower speeds enable prey to use their maximum manoeuvring capacity and favour prey survival, and that the predator needs to be more athletic than its prey to sustain a viable success rate.