Short-term effects of music stimulus on enhancement of cognitive functions in human brain are documented, however the underlying neural mechanisms in these cognitive effects are not well investigated. In this study, we have attempted to decipher the mechanisms involved in alterations of neural networks that lead to enhanced cognitive effects post-exposure to music. We have investigated the changes in Electroencephalography (EEG) power and functional connectivity of alpha band in resting state of the brain after exposure to Indian classical music. We have quantified the changes in functional connectivity by phase coherence, phase delay, and phase slope index analyses. Spatial mapping of functional connectivity dynamics thus obtained, on brain networks revealed reduced information flow in long-distance connections between frontal and parietal cortex, and between other cortical regions underpinning intelligence. Analyses also showed increased power in the prefrontal and occipital cortex. With these findings, we have developed a stimulus-mechanism-end effect based neuro-cognitive model that explains the music induced cognitive enhancement by a three-channel framework - (1) enhanced global efficiency of brain, (2) enhanced local neural efficiency at the prefrontal lobe, and (3) increased sustained attention. Results signify that music directly affects the cognitive system and leads to improved brain efficiency through well-defined mechanisms.