This paper introduces and exploits a hybrid numerical approach for fully resolved numerical simulations of reactive mixing in T-shaped microreactors and thereby enables a computational analysis of how chemical reactions interact with convective and diffusive transport. The approach exploits the fast redirection of the flow inside the mixing channel, resulting in a flow field with positive axial flow component everywhere after a short entry zone. This allows handling the axial flow direction as a pseudo-time variable, so that the evolution of the concentration profile can be computed consecutively on successive cross sections, following the main axial flow direction. With this approach the finest length scales, given by the Batchelor length scale, can be resolved for such a reactive mixing process inside a T-microreactor at stationary flow conditions. This allows for a detailed analysis of the mixing state as well as important characteristics of the reactive mixing process like yield and selectivity. The concrete numerical simulations yield local diffusion times inside the reactor, reveal the influence of the strength of the secondary flow on the progress of the chemical reaction and show how local selectivities result from the species transport.