The unique engulfment filtration strategy of microphagous rorqual whales has evolved relatively recently (<5 Ma) and exploits extreme predator/prey size ratios to overcome the maneuverability advantages of swarms of small prey, such as krill. Forage fish, in contrast, have been engaged in evolutionary arms races with their predators for more than 100 million years and have performance capabilities that suggest they should easily evade whale-sized predators, yet they are regularly hunted by some species of rorqual whales. To explore this phenomenon, we determined, in a laboratory setting, when individual anchovies initiated escape from virtually approaching whales, then used these results along with in situ humpback whale attack data to model how predator speed and engulfment timing affected capture rates. Anchovies were found to respond to approaching visual looming stimuli at expansion rates that give ample chance to escape from a sea lion-sized predator, but humpback whales could capture as much as 30-60% of a school at once because the increase in their apparent (visual) size does not cross their prey's response threshold until after rapid jaw expansion. Humpback whales are, thus, incentivized to delay engulfment until they are very close to a prey school, even if this results in higher hydrodynamic drag. This potential exaptation of a microphagous filter feeding strategy for fish foraging enables humpback whales to achieve 7× the energetic efficiency (per lunge) of krill foraging, allowing for flexible foraging strategies that may underlie their ecological success in fluctuating oceanic conditions.