We present 2.5-dimensional radiation-hydrodynamics simulations of the accretion-induced collapse ( AIC) of white dwarfs, starting from two-dimensional rotational equilibrium configurations, thereby accounting consistently for the effects of rotation prior to and after core collapse. We focus our study on a 1.46 and a 1.92 M-circle dot a model. Electron capture leads to the collapse to nuclear densities of these cores a few tens of milliseconds after the start of the simulations. The shock generated at bounce moves slowly, but steadily, outward. Within 50 - 100 ms, the stalled shock breaks out of the white dwarf along the poles. The blast is followed by a neutrino-driven wind that develops within the white dwarf, in a cone of similar to 40 degrees opening angle about the poles, with a mass loss rate of ( 5 8); 10(-3) M-circle dot s(-1). The ejecta have an entropy on the order of ( 20 - 50) k(B) baryon(-1) and an electron fraction that is bimodal. By the end of the simulations, at greater than or similar to 600 ms after bounce, the explosion energy has reached ( 3 4); 1049 ergs and the mass has reached a few times 10(-3) M-circle dot. We estimate the asymptotic explosion energies to be lower than 1050 ergs, significantly lower than those inferred for standard core collapse. The AIC of white dwarfs thus represents one instance where a neutrino mechanism leads undoubtedly to a successful, albeit weak, explosion. We document in detail the numerous effects of the fast rotation of the progenitors: the neutron stars are aspherical; the "nu(mu)" and (nu) over bar (e) neutrino luminosities are reduced compared to the nu(e) neutrino luminosity; the deleptonized region has a butterfly shape; the neutrino flux and electron fraction depends strongly upon latitude ( a la von Zeipel); and a quasi-Keplerian 0.1 - 0.5 M-circle dot accretion disk is formed.