Developing facile, green, and efficient synthetic methodology for preparing surface‐functionalized nanogels has attracted tremendous attention in the field of polymer chemistry and biomaterials engineering. Herein, a series of “clickable” P(MAA‐PMA) nanogels with reactive alkyne groups were conveniently prepared by “one‐pot” reflux‐precipitation polymerization (RPP), their particle sizes and zeta potentials are solid content‐dependent. Using P(MAA‐PMA)‐1 nanogels as the model, the physicochemical properties including particle size, surface potential, morphology, solution stability, and pH/redox responsiveness were characterized in detail. Moreover, the pH/redox dual‐responsive drug release feature/kinetics and parameters were analyzed using Korsmeyer–Peppas model and Gallagher–Corrigan model. Then the surface of nanogels was facilely modified with various thiol‐containing functional ligands via thiol‐yne photo click reaction. As targeted drug carriers, doxorubicin (DOX)‐loaded folic acid (FA)‐functionalized nanogels (FA@Nanogels/DOX) demonstrated higher tumor cell proliferation inhibition effect in B16F10 cancer cells than that in CHO‐K1 normal cells, while the non‐FA‐functionalized counterparts (Nanogels/DOX) do not show similar effect. This work provides a versatile “one‐pot RPP‐photo Click functionalization” strategy to construct surface‐functionalized pH/redox dual responsive nanogels for efficient and targeted drug delivery.