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A novel mechanism of the bistablity onset based on a low-frequency modulation of the natural frequency of a harmonically forced nonlinear oscillator is presented. It is shown that such modulation results in arising of an additional bistable state, which has a lower threshold for bistability with respect to the forcing amplitude as compared to the modulationless case. This lowering is caused by the high- to low-frequency interaction. A theory of this phenomenon is presented by considering dynamics of the Duffing oscillator as an example. The corresponding threshold values of the amplitude are found analytically. A comparative analysis of different types of bistable states in such oscillator is carried out as well. The results are important for such applications like storing binary data in digital electronics.