We consider the spatio-temporal behavior of the A+B --> 0 bimolecular reaction in a system where both reactants tend to segregate into separated phases. Our study is based on the numerical solution of a pair of reaction-diffusion equations appropriate to capture the underlying coarsening dynamics. The interplay between reaction and coarsening leads to a complex pattern of reactants spatial distribution. At short/intermediate times two distinctive dynamical regimes are seen in the decay of overall concentration and droplet number and the behavior of droplet radii.