The elliptic (v_{2}) and triangular (v_{3}) azimuthal anisotropy coefficients in central ^{3}He+Au, d+Au, and p+Au collisions at sqrt[s_{NN}]=200 GeV are measured as a function of transverse momentum (p_{T}) at midrapidity (|η|<0.9), via the azimuthal angular correlation between two particles both at |η|<0.9. While the v_{2}(p_{T}) values depend on the colliding systems, the v_{3}(p_{T}) values are system independent within the uncertainties, suggesting an influence on eccentricity from subnucleonic fluctuations in these small-sized systems. These results also provide stringent constraints for the hydrodynamic modeling of these systems.