In this article, a class of singularly perturbed 2D parabolic convection-diffusion-reaction initial-boundary-value problem is numerically solved by the alternating direction implicit type operator splitting streamline-diffusion finite element method. The proposed scheme alleviates the computational complexity and the high storage requirement for higher-dimensional problems. The overall stability of the two-step method is established. A piecewise-uniform Shishkin mesh is used for the spatial domain discretization. ε-uniform error estimate has been derived with an appropriate choice of the stabilization parameter. The parameter is shown to depend on the time step-length which is necessary for the stability of the method. Some numerical simulations are carried out to validate the theoretical error estimate.