We demonstrate a time-resolved single-photon detection technique based on ultrafast sum-frequency generation, providing femtosecond measurement capability for single photons in photonic quantum information processing. Noncollinear broadband upconversion in periodically poled MgO-doped stoichiometric lithium tantalate with an ultrafast pump and detection with a Si single-photon counter enable efficient detection of IR photons and temporal resolution of ~150 fs. We utilize the timing resolution to map the generation efficiency profile along the propagation axis of a periodically poled KTiOPO(4) crystal, revealing its local grating quality with millimeter resolution. We also apply the technique to two-photon coincidence measurements and directly demonstrate time anticorrelation between coincident-frequency entangled photons that are parametrically generated under extended phase-matching conditions.