We used network-based diffusion analysis to reveal the cultural spread of a naturally occurring foraging innovation, lobtail feeding, through a population of humpback whales (Megaptera novaeangliae) over a period of 27 years. Support for models with a social transmission component was 6 to 23 orders of magnitude greater than for models without. The spatial and temporal distribution of sand lance, a prey species, was also important in predicting the rate of acquisition. Our results, coupled with existing knowledge about song traditions, show that this species can maintain multiple independently evolving traditions in its populations. These insights strengthen the case that cetaceans represent a peak in the evolution of nonhuman culture, independent of the primate lineage.