Since the first exfoliation and identification of graphene in 2004, research on layered ultrathin two-dimensional (2D) nanomaterials has achieved remarkable progress. Realizing the special importance of 2D geometry, we demonstrate that the controlled synthesis of nonlayered nanomaterials in 2D geometry can yield some unique properties that otherwise cannot be achieved in these nonlayered systems. Herein, we report a systematic study involving theoretical and experimental approaches to evaluate the Li-ion storage capability in 2D atomic sheets of nonlayered molybdenum dioxide (MoO2). We develop a novel monomer-assisted reduction process to produce high quality 2D sheets of nonlayered MoO2. When used as lithium-ion battery (LIB) anodes, these ultrathin 2D-MoO2 electrodes demonstrate extraordinary reversible capacity, as high as 1516 mAh g-1 after 100 cycles at the current rate of 100 mA g-1 and 489 mAh g-1 after 1050 cycles at 1000 mA g-1. It is evident that these ultrathin 2D sheets did not follow the normal intercalation-cum-conversion mechanism when used as LIB anodes, which was observed for their bulk analogue. Our ex situ XPS and XRD studies reveal a Li-storage mechanism in these 2D-MoO2 sheets consisting of an intercalation reaction and the formation of metallic Li phase. In addition, the 2D-MoO2 based microsupercapacitors exhibit high areal capacitance (63.1 mF cm-2 at 0.1 mA cm-2), good rate performance (81% retention from 0.1 to 2 mA cm-2), and superior cycle stability (86% retention after 10,000 cycles). We believe that our work identifies a new pathway to make 2D nanostructures from nonlayered compounds, which results in an extremely enhanced energy storage capability.