It is a challenge to meld the energy of secondary batteries with the power of supercapacitors. Herein, we created electrodes finely tuned for this purpose, consisting of a monolayer of MnO nanocrystallites mechanically anchored by pore-surface terminations of 3D arrays of graphene-like carbon nanosheets ("3D-MnO/CNS"). The biomass-derived carbon nanosheets should offer a synthesis cost advantage over comparably performing designer nanocarbons, such as graphene or carbon nanotubes. High Li storage capacity is achieved by bulk conversion and intercalation reactions, while high rates are maintained through stable ∼20 nm scale diffusion distances. For example, 1332 mAh g(-1) is reached at 0.1 A g(-1), 567 mAh g(-1) at 5 A g(-1), and 285 mAh g(-1) at 20 A g(-1) with negligible degradation at 500 cycles. We employed 3D-MnO/CNS (anode) and carbon nanosheets (cathode) to create a hybrid capacitor displaying among the most promising performances reported: based on the active materials, it delivers 184 Wh kg(-1) at 83 W kg(-1) and 90 Wh kg(-1) at 15 000 W kg(-1) with 76% capacity retention after 5000 cycles.