Surface microrollers are promising microrobotic systems for controlled navigation in the circulatory system thanks to their fast speeds and decreased flow velocities at the vessel walls. While surface propulsion on the vessel walls helps minimize the effect of strong fluidic forces, three-dimensional (3D) surface microtopography, comparable to the size scale of a microrobot, due to cellular morphology and organization emerges as a major challenge. Here, we show that microroller shape anisotropy determines the surface locomotion capability of microrollers on vessel-like 3D surface microtopographies against physiological flow conditions. The isotropic (single, 8.5 µm diameter spherical particle) and anisotropic (doublet, two 4 µm diameter spherical particle chain) magnetic microrollers generated similar translational velocities on flat surfaces, whereas the isotropic microrollers failed to translate on most of the 3D-printed vessel-like microtopographies. The computational fluid dynamics analyses revealed larger flow fields generated around isotropic microrollers causing larger resistive forces near the microtopographies, in comparison to anisotropic microrollers, and impairing their translation. The superior surface-rolling capability of the anisotropic doublet microrollers on microtopographical surfaces against the fluid flow was further validated in a vessel-on-a-chip system mimicking microvasculature. The findings reported here establish the design principles of surface microrollers for robust locomotion on vessel walls against physiological flows.