Antisymmetric Dzyaloshinskii-Moriya (DM) interactions generating from the spin-orbit coupling induce various fascinating properties, like magnetoelectric (ME) effect, weak ferromagnetism and non-trivial topological spin textures like skyrmions, in real materials. Compared to their symmetric isotropic exchange counterpart, these interactions are generally of a weaker order of strength, creating modest twisting in the spin structure which results in weak ferromagntism or weak linear ME effect. Our proposed two-sublattice model, in contrast, predicts a hitherto unobserved, charge ordered non-collinear ferrimagnetic behavior with a considerably high magnetization M coexisting with a ferroelectric (FE) order with an electric polarization P and a strong cross coupling between them which is primarily driven by the inter-sublattice DM interactions. The key to realize these effects is the coupling between these microscopic interactions and the FE primary order parameter. We predict microscopic mechanisms to achieve electric field E induced spin-reorientation transitions and 180 • switching of the direction of M. This model was realized in the hexagonal phase of LuFeO3 doped with electrons. This system shows P ∼ 15 µC/cm 2 , M ∼ 1.3 µB/Fe and magnetic transition near room temperature (∼ 290 K). Our theoretical results are expected to stimulate further quest for energy-efficient routes to control magnetism for spintronics applications.