Two-dimensional (2D) magnets have broad application prospects in the spintronics, but how to effectively control them with a small electric field is still an issue. Here we propose that 2D magnets can be efficiently controlled in a multiferroic heterostructure composed of 2D magnetic material and perovskite oxide ferroelectric (POF) whose dielectric polarization is easily flipped under a small electric field. We illustrate the feasibility of such strategy in the bilayer CrI₃/BiFeO₃(001) heterostructure by using the first-principles calculations. Different from the traditional POF multiferroic heterostructures which have strong interface interactions, we find that the interface interaction between CrI₃ and BiFeO₃(001) is van der Waals type. Whereas, the heterostructure has particular strong magnetoelectric coupling where the bilayer CrI₃ can be efficiently switched between ferromagnetic and antiferromagnetic types by the polarized states P↑ and P↓ of BiFeO₃(001). We also discover the competing effect between electron doping and the additional electric field on the interlayer exchange coupling interaction of CrI₃, which is responsible to the magnetic phase transition. Our results provide a avenue for the tuning of 2D magnets with a small electric field. See: https://www.nature.com/articles/s41524-022-00706-w