<p>Chiral state transfers (CSTs) associated with exceptional points are always under the scrutiny of theoretical and experimental science, owing to its exotic physics and fascinating potential applications. In conventional wisdom, CSTs require adiabatically steering the non-Hermitian Hamiltonian in the parameter space, which inevitably leads to ultra-complex experimental setups and long evolution times, thereby exhibiting a bottleneck in integrating them into compact devices. Here, through both theoretical analysis and circuit-based experiments, we demonstrate nonlinear-exceptional-point-associated chiral-like state transfer, wherein the final state depends on the direction of parameter steering. Notably, our scheme does not require adiabatic evolution. In particular, the steering trajectory can be effectively reduced to three distinct points by varying a single parameter in the parameter space, thereby significantly lowering the experimental complexity. We show that these nonlinear chiral-like state transfers (NCSTs) in our system strictly arise from the basins of attraction for the stable states of nonlinear Hamiltonians, and have no counterparts in linear (non-) Hermitian systems. Our finding transforms the fundamental understanding of CSTs, and may open up new avenues for miniaturizing various relevant applications.</p>