Transition metal sulfides (TMSs) have been widely explored as electrode materials for supercapacitors (SCs). Nevertheless, the application of TMSs alone is limited due to their lattice expansion and dissolution in an alkaline electrolyte. To overcome these challenges, in this study, hierarchical core–shell hollow Co₃S₄@NiCo₂O₄ nanosheet arrays have been constructed on reduced graphene oxide/nickel foam (rGO/NF) through a metal–organic framework (MOF)-engaged strategy. The MOF-derived two-dimensional (2D) hollow Co₃S₄ nanosheets can offer rich electroactive sites and rapid charge transport paths. The 2D NiCo₂O₄ nanosheets with high electrochemical activity and a stable lattice can overcome the intrinsic defects of Co₃S₄ by coating on its surface. Besides, the binder-free configuration ensures good electronic conductivity and mechanical stability. Thus, the Co₃S₄@NiCo₂O₄/rGO/NF exhibits a significantly improved specific capacitance (6.34 F cm⁻² at 2 A cm⁻²), rate capability (57.9% at 50 mA cm⁻²) and cycling durability (70.9%, after 5000 cycles), compared with Co₃S₄/rGO/NF. Moreover, the Co₃S₄@NiCo₂O₄/rGO/NF and an activated carbon (AC) electrode have been constructed into an asymmetric supercapacitor (ASC), which exhibits an excellent energy density (35.7 W h kg⁻¹ at a power density of 799.3 W kg⁻¹) and an outstanding cycling stability (85.7% capacitance retention after 10 000 cycles) and a high coulombic efficiency (95%). Two solid-state ASCs can power four green light emitting diode (LED) bulbs for 4 min, demonstrating the great potential of the Co₃S₄@NiCo₂O₄/rGO/NF electrode in practical applications.