The Yin–Yang grid, while offering advantages such as quasi-uniformity and pole-singularity avoidance, inherently lacks global conservation owing to interpolation at grid boundaries. To address this problem, we proposed a compact flux correcting method to ensure conservation based on a third-order multimoment constrained finite volume scheme. Using the nine point values within each computational cell, a bivariate quadratic polynomial was constructed for high-fidelity boundary interpolation and flux reconstruction. Identical flux across the boundary of overlapped grids was enforced in the Yin and Yang components with the help of the polynomial. A third-order conservative advection scheme was therefore achieved on the Yin–Yang grid, effectively balancing numerical accuracy and computational efficiency. Several standard numerical tests were conducted to confirm the performance of the interpolation algorithm and the conservation calculation scheme. Results revealed that the high accuracy and the stability of the strict conservation scheme are helpful in passive transport situations on Yin–Yang grids.