In low-income populations, neglected diseases are the principal cause of mortality. Of these, leishmaniasis and malaria, being parasitic, protozoan infections, affect millions of people worldwide and are creating a public health problem. The present work evaluates the leishmanicidal and antiplasmodial action of a series of twelve p-coumaric acid derivatives. Of the tested derivatives, eight presented antiparasitic activities 1–3, 8–12. The hexyl p-coumarate derivative (9) (4.14 ± 0.55 μg/mL; selectivity index (SI) = 2.72) showed the highest leishmanicidal potency against the Leishmania braziliensis amastigote form. The results of the molecular docking study suggest that this compound inhibits aldehyde dehydrogenase (ALDH), mitogen-activated kinase protein (MPK4), and DNA topoisomerase 2 (TOP2), all of which are key enzymes in the development of Leishmania braziliensis. The data indicate that these enzymes interact via Van der Waals bonds, hydrophobic interactions, and hydrogen bonds with phenolic and aliphatic parts of this same compound. Of the other compounds analyzed, methyl p-coumarate (64.59 ± 2.89 μg/mL; IS = 0.1) demonstrated bioactivity against Plasmodium falciparum. The study reveals that esters presenting a p-coumarate substructure are promising for use in synthesis of derivatives with good antiparasitic profiles.