In this study, the authors investigate the problem of the stochastically finite-time stability analysis and control design of an adaptive single-input and single-output (SISO) uncertain stochastic non-linear system via establishing a new stability criterion. Owing to the unknown dynamics and unmeasured system variables, fuzzy logic systems and a fuzzy state observer are constructed and applied to identify the stochastic system, respectively. Combining the finite-time definition, stochastic differential equation and o^ formula, a novel stochastically finite-time stability theorem is raised in this study. By utilising the novel criterion and adaptive backstepping intelligent control, a stochastically finite-time control method is proposed. It is illustrated that the controlled stochastic system is semi-global finite-time stable in probability and behaves excellent convergence. The simulation results of a two-stage continuous stirred tank reactor process reveal the validity and efficiency.