A method for modeling the effects of finite-rate chemistry such as partial extinctions and reignitions is developed and used to compute turbulent CO/H-2/N-2 or CH4-air-piloted jet diffusion flames close to extinction. The method is combined with a two-dimensional Large Eddy Simulation procedure employing a partial equilibrium/two-scalar exponential Probability Density Function (PDF) combustion submodel applied at the subgrid scale (SCS) level. Subgrid motions are modeled with a First-order closure utilizing an anisotropic subgrid eddy-viscosity and two equations for the subgrid scale turbulent kinetic and scalar energies. Statistical independence of the joint PDF scalars is here avoided and the required moments are obtained from an extended scale-similarity assumption. Extinction is determined by comparing the local Damkohler number against a 'critical' local limit related to the Gibson scalar scale and the reaction zone thickness. The post-extinction regime is treated with a reactedness progress variable computed from a Lagrangian transport equation and a two-scaler reactedness-mixture fraction presumed PDF. Comparisons with well documented turbulent flame data suggested the ability of the presented methodology to describe many experimental trends and variations of the momentum and reactive scalar mixing fields at flame conditions close to extinction.