Molecular interaction in two-dimensional (2D) van der Waals (vdW) interfaces has drawn tremendous attention for extraordinary materials characteristics. So far sensing characteristics of molecular interaction has been exploited extensively to reach the detection limit to a few parts-per-billion (ppb) of molecules and far less attention is given to the evolution of persistent current state due to the molecular exposure. Our study focuses on molecular memory operation of MoS₂-graphene heterostructure based field effect transistor. Metastable resistance state of the device due to the external perturbation of molecules is tuned to get a nearly relaxation free current state at much lower molecular concentration of 10 ppb to facilitate non-volatile memory features for molecular memory operation. An ultrafast switching operation in milli-second order is achieved at room temperature for the fastest recovery obtained so far in any molecular sensor. The process is co-controlled both by molecular as well as external charge density.