Residual-based variational multiscale (RBVMS) methods provide a systematic framework for stabilizing advection-dominated partial differential equations within variational discretizations. In this work, we extend RBVMS concepts to cell-centered FVM by exploiting the intrinsic scale separation induced by control-volume averaging, which may be interpreted as an implicit box filter. This discrete filtering naturally decomposes the solution into grid-scale and subgrid-scale components without introducing explicit spatial filtering operations, thereby avoiding commutation errors between the filter and divergence operators. Starting from the strong-form residual of the governing equations, the subgrid scales are modeled analytically in terms of the classical grid- and time-step-dependent stabilization parameter in RBVMS. This leads to residual-based corrections that appear as additional fluxes in the finite volume equations. The resulting formulation may be interpreted as a streamline-upwind finite volume (SUFV) method that retains consistency with the underlying differential equations while selectively stabilizing advection-dominated directions. The method is assessed using the advection skew to the mesh and the Molenkamp rotating-cone benchmarks over a range of cell Peclet numbers. The proposed SUFV formulation exhibits near-second-order convergence in the L₁ norm, substantially reduced numerical diffusion relative to upwind schemes, and improved robustness compared to central differencing, which develops nonphysical oscillations in strongly advection-dominated regimes. The inclusion of the temporal derivative term in the residual-based subgrid-scale model is shown to enhance accuracy without compromising stability, as has been shown in the finite element setting. These results demonstrate that RBVMS concepts can be systematically transferred to the cell-centered FVM for advection-dominated problems. Ongoing work focuses on extending the present framework to 3D scalar transport and momentum equations and exploring its application to large-eddy simulations.