Radial substructures in circumstellar disks are now routinely observed by ALMA. There is also growing evidence that disk winds drive accretion in such disks. We show through 2D (axisymmetric) simulations that rings and gaps develop naturally in magnetically coupled disk-wind systems on the scale of tens of au, where ambipolar diffusion (AD) is the dominant non-ideal MHD effect. In simulations where the magnetic field and matter are moderately coupled, the disk remains relatively laminar with the radial electric current steepened by AD into a thin layer near the midplane. The toroidal magnetic field sharply reverses polarity in this layer, generating a large magnetic torque that drives fast accretion, which drags the poloidal field into a highly pinched radial configuration. The reconnection of this pinched field creates magnetic loops where the net poloidal magnetic flux (and thus the accretion rate) is reduced, yielding dense rings. Neighbouring regions with stronger poloidal magnetic fields accrete faster, forming gaps. In better magnetically coupled simulations, the so-called `avalanche accretion streams' develop continuously near the disk surface, rendering the disk-wind system more chaotic. Nevertheless, prominent rings and gaps are still produced, at least in part, by reconnection, which again enables the segregation of the poloidal field and the disk material similar to the more diffusive disks. However, the reconnection is now driven by the non-linear growth of MRI channel flows. The formation of rings and gaps in rapidly accreting yet laminar disks has interesting implications for dust settling and trapping, grain growth, and planet formation.