The pursuit of prey is vital to the biology of a predator and many aspects of predatorybehavior are well-studied. However, it is unclear how a pursuit can be effective when the prey is faster than a predator. Using kinematic measurements, we considered the strategy of red lionfish (Pterois volitans) and devil lionfish (Pterois miles) as they pursued a variety of prey fishes. Despite generally swimming slower than their prey, red lionfish and devil lionfish succeeded in capturing prey in 61% and 82% of our experiments. This successful pursuit behavior was defined by uninterrupted motion and a targeting strategy of pure pursuit, characterized by heading towards the prey’s position and not the anticipated point of interception. These characteristics comprise a behavior that we call the ‘persistent-predation strategy’, which may be exhibited by a diversity of predators with relatively slow locomotion. When encountering lionfish, prey avoidance behavior was variable among species, but without a consistency that was predictive of the outcome of an interaction. The coupled nature of these interactions challenge the ability to resolve what aspects of performance matter during predator-prey interactions. To address this challenge, we developed a 2D agent-based mathematical model for a fish predator and an individual prey fish enclosed within a circular arena. We parameterized and tested the predictions of this model with experimental measurements of fish trajectories and performed numerical simulations with a Monte-Carlo approach to predict the trajectories of predator and prey. By manipulating single parameters, we were able to determine the effect that each parameter had on the outcome of a simulated interaction. We found that metrics related to vigilance and evasion strategy may be more valuable toward evading a slow predator than maximal measure of kinematic performance. This method demonstrates the power of agent-based mathematical modeling for testing hypotheses about the salient features that determine the outcome of predator-prey interactions.