Synaptic plasticity underlies the brain’s ability to learn and adapt. This process is often studied in small groups of neurons in vitro or indirectly through its effects on behavior in vivo. Due to the limitations of available experimental techniques, investigating synaptic plasticity at the micro-circuit level relies on simulation-based approaches. Although modeling studies provide valuable insights, they are usually limited in scale and generality. To overcome these limitations, we extended a previously published and validated large-scale cortical network model with a recently developed calcium-based model of functional plasticity between excitatory cells. We calibrated the network to mimic an in vivo state characterized by low synaptic release probability and low-rate asynchronous firing, and exposed it to ten different stimuli. We found that synaptic plasticity sparsely and specifically strengthened synapses forming spatial clusters on postsynaptic dendrites and those between populations of co-firing neurons, also known as cell assemblies: among 312 million synapses, only 5% experienced noticeable plasticity and cross-assembly synapses underwent three times more changes than average. Furthermore, as occasional large-amplitude potentiation was counteracted by more frequent synaptic depression, the network remained stable without explicitly modeling homeostatic plasticity. When comparing the network’s responses to the different stimuli before and after plasticity, we found that it became more stimulus-specific after plasticity, manifesting in prolonged activity after selected stimuli and more unique groups of neurons responding exclusively to a single pattern. Taken together, we present the first stable simulation of Hebbian plasticity without homeostatic terms at this level of detail and analyze the rules determining the sparse changes.