Static current profile control (CPC) is shown numerically to substantially enhance plasma confinement in the reversed-field pinch (RFP). By suitable application of an auxiliary electric field and adjustment of its internal location, width and amplitude, strongly decreased levels of dynamo fluctuations are obtained. The simulations are performed using a fully non-linear, resistive magnetohydrodynamic model, including the effects of ohmic heating as well as parallel and perpendicular heat conduction along stochastic field lines. The importance of controlling the parallel current profile in the core plasma to minimize the effects of tearing modes on confinement is thus confirmed. A near three-fold increase in energy confinement is found and poloidal plasma beta increases by 30% from 0.20 to 0.27. The edge heat flux is reduced to a third of that of the conventional RFP. The high-confinement phase is interrupted here by a crash, characterized by a rapid decrease in confinement. A detailed study of the crash phase is carried out by the standard Δ' theory and a fully resistive linearized time-spectral method; the generalized weighted residual method. The analysis suggests that the instability is caused by pressure-driven, resistive g-modes. Inclusion of anisotropic thermal conduction reduces the linear growth rates. As compared with our earlier numerical studies of CPC in the RFP, employing feedback control, the present static control scheme should be more easily implemented experimentally.