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Brain models typically focus either on low-level biological detail or on qualitative behavioral effects. In contrast, we present a biologically-plausible spiking-neuron model of associative learning and recognition that accounts for both human behavior and low-level brain activity across the whole task. Based on cognitive theories and insights from machine-learning analyses of M/EEG data, the model proceeds through five processing stages: stimulus encoding, familiarity judgement, associative retrieval, decision making, and motor response. The results matched human response times and source-localized MEG data in occipital, temporal, prefrontal, and precentral brain regions; as well as a classic fMRI effect in prefrontal cortex. This required two main conceptual advances: a basal-ganglia-thalamus action-selection system that relies on brief thalamic pulses to change the functional connectivity of the cortex, and a new unsupervised learning rule that causes very strong pattern separation in the hippocampus. The resulting model shows how low-level brain activity can result in goal-directed cognitive behavior in humans.