The nonclassical light sources, such as frequency-time entangled photons, are anticipated to offer significant benefits for emerging quantum optical sensing or spectroscopic measurements and manifest on ultrafast time scales (sub-ps to fs). However, the constrained time resolution (ns to ps) of photon-counting detectors poses challenges in comprehensively characterizing their detailed properties on ultrafast time scales. Therefore, we present a novel asynchronous optical sampling (ASOPS) technique utilizing two-color optical frequency combs to demonstrate highly precise and sensitive ultrafast time-resolved cross-correlation measurements at the single-photon level. By employing photon counting statistics, this method successfully reconstructed the picosecond pulse width cross-correlation waveforms at extremely low power level (<1 photon per pulse), while effectively suppressing the residual temporal jitter between the two combs via optically triggered averaging using asynchronous optical sampling of combs. The use of repetition frequency stabilized distinct-wavelength pulses allowed for the effective suppression of strong background light from the pump through spectral filtering, achieving single-photon sensitivity. Subsequently, we parametrically down converted the frequency doubled light from the Er comb in the nonlinear ppKTP waveguide to generate quantum entangled photons at telecom band. A 9.04% Klyshko efficiency with a photon pair generation rate of 0.98 MHz/mW was obtained using heralding detection. Employing the established ASOPS technique to the generated photon pairs enabled the realization of ultrafast time-resolved and quantum mechanical correlation measurements. This paves the way for a versatile and comprehensive manipulation of quantum-entangled photon pairs in the time-domain, with potential applications in ultrafast optical quantum technology and ultrashort fluorescence measurements.