Mapping red blood cells (RBCs) flow and oxygenation is of key importance for analyzing brain and tissue physiology. Current microscopy methods are limited either in sensitivity or in spatio-temporal resolution. In this work, we introduce a novel approach based on label-free third-order sum-frequency generation (TSFG) and third-harmonic generation (THG) contrasts. First, we propose a novel experimental scheme for color TSFG microscopy, which provides simultaneous measurements at several wavelengths encompassing the Soret absorption band of hemoglobin. We show that there is a strong three-photon (3P) resonance related to the Soret band of hemoglobin in THG and TSFG signals from zebrafish and human RBCs, and that this resonance is sensitive to RBC oxygenation state. We demonstrate that our color TSFG implementation enables specific detection of flowing RBCs in zebrafish embryos and is sensitive to RBC oxygenation dynamics with single-cell resolution and microsecond pixel times. Moreover, it can be implemented on a 3P microscope and provides label-free RBC-specific contrast at depths exceeding 600 µm in live adult zebrafish brain. Our results establish a new multiphoton contrast extending the palette of deep-tissue microscopy.