The smallest algae, less than 3 μm in diameter, are the most abundant eukaryotes of the World Ocean. Their feeding on planktonic bacteria of similar size is globally important but physically enigmatic. Tiny algal cells tightly packed with the voluminous chloroplasts, nucleus, and mitochondria appear to have insufficient organelle-free space for prey internalization. Here, we present the first direct observations of how the 1.3-μm algae, which are only 1.6 times bigger in diameter than their prey, hold individual Prochlorococcus cells in their open hemispheric cytostomes. We explain this semi-extracellular phagocytosis by the cell size limitation of the predatory alga, identified as the Braarudosphaera haptophyte with a nitrogen (N2)-fixing endosymbiont. Because the observed semi-extracellular phagocytosis differs from all other types of protistan phagocytosis, we propose to name it "pomacytosis" (from the Greek πώμα for "plug").