All attempts at treating strokes by pharmacologically reducing the human brain's vulnerability to ischaemia have failed, leaving stroke as a leading cause of death, disability and massive socioeconomic loss worldwide. Over decades, research has failed to translate over 1,000 experimental treatments from discovery in cells and rodents to use in humans, a scientific crisis that gave rise to the prevailing belief that pharmacological neuroprotection is not feasible or practicable in higher-order brains. To provide a strategy for advancing stroke therapy, we used higher-order gyrencephalic non-human primates, which bear genetic, anatomical and behavioural similarities to humans and tested neuroprotection by PSD-95 inhibitors--promising compounds that uncouple postsynaptic density protein PSD-95 from neurotoxic signalling pathways. Here we show that stroke damage can be prevented in non-human primates in which a PSD-95 inhibitor is administered after stroke onset in clinically relevant situations. This treatment reduced infarct volumes as gauged by magnetic resonance imaging and histology, preserved the capacity of ischaemic cells to maintain gene transcription in genome-wide screens of ischaemic brain tissue, and significantly preserved neurological function in neurobehavioural assays. The degree of tissue neuroprotection by magnetic resonance imaging corresponded strongly to the preservation of neurological function, supporting the intuitive but unproven dictum that integrity of brain tissue can reflect functional outcome. Our findings establish that tissue neuroprotection and improved functional outcome after stroke is unequivocally achievable in gyrencephalic non-human primates treated with PSD-95 inhibitors. Efforts must ensue to translate these findings to humans.