Astrocytes have been shown to modulate synaptic transmission and plasticity in specific cortical synapses, but our understanding of the underlying molecular and cellular mechanisms remains limited. Here we present a new biophysicochemical model of a somatosensory cortical layer 4 to layer 2/3 synapse to study the role of astrocytes in spike-timing-dependent long-term depression (t-LTD) in vivo. By applying the synapse model and electrophysiological data recorded from rodent somatosensory cortex, we show that a signal from a postsynaptic neuron, orchestrated by endocannabinoids, astrocytic calcium signaling, and presynaptic N-methyl-D-aspartate receptors coupled with calcineurin signaling, induces t-LTD which is sensitive to the temporal difference between post- and presynaptic firing. We predict for the first time the dynamics of astrocyte-mediated molecular mechanisms underlying t-LTD and link complex biochemical networks at presynaptic, postsynaptic, and astrocytic sites to the time window of t-LTD induction. During t-LTD a single astrocyte acts as a delay factor for fast neuronal activity and integrates fast neuronal sensory processing with slow non-neuronal processing to modulate synaptic properties in the brain. Our results suggest that astrocytes play a critical role in synaptic computation during postnatal development and are of paramount importance in guiding the development of brain circuit functions, learning and memory.