Simulating plasma-assisted combustion represents a considerable challenge due to the large discrepancy of the time scales involved. While the turbulent eddy time scales are of the order of microseconds, the plasma sheath time scales are 3-4 orders of magnitude lower. Contrarily to the chemical reactions, the stiffness of the plasma equations can not be relieved simply by using an implicit integration strategy, thus leading to excessive computational effort even for the simplest cases. Recently, it was shown that this hurdle can be overcome by recasting the plasma driftdiffusion transport equations such that the potential is not obtained from Gauss’s law directly but rather from Ohm’s law. Such a recast is performed while still ensuring that Gauss’s law is satisfied and thus does not modify the physics of the drift-diffusion model in any way. In this paper, we use this novel approach to integrate, for the first time, a plasma discharge in fully coupled form with the turbulent hydrogen/air mixing layer and combustion process taking place in the combustor of a scramjet flying at Mach 11. The chemical model includes electrons, 7 different types of ions, 11 neutral species and 79 reactions. Results indicate that more than 5 discharges need to be performed before achieving a self-repeating pattern due to the strong coupling between the flow, combustion, and plasma. Further, the plasma-assisted flame anchoring is seen to create a recirculation region of significant size within the turbulent boundary layer which affects skin friction and heat loads considerably.