Time-domain diffuse correlation spectroscopy (TD-DCS) offers a novel approach to high-spatial resolution functional brain imaging based on the direct quantification of cerebral blood flow (CBF) changes in response to neural activity. However, the signal-to-noise ratio (SNR) offered by previous TD-DCS instruments remains a challenge to achieving the high temporal resolution needed to resolve perfusion changes during functional measurements. Here we present a next-generation optimized functional TD-DCS system that combines a custom 1,064 nm pulse-shaped, quasi transform-limited, amplified laser source with a high-resolution time-tagging system and superconducting nanowire single-photon detectors (SNSPDs). System characterization and optimization was conducted on homogenous and two-layer intralipid phantoms before performing functional CBF measurements in six human subjects. By acquiring CBF signals at over 5 Hz for a late gate start time of the temporal point spread function (TPSF) at 15 mm source-detector separation, we demonstrate for the first time the measurement of blood flow responses to breath-holding and functional tasks using TD-DCS.