In this paper, a reduced order model based on the Proper Generalized Decomposition (PGD) is applied to the numerical modeling of the incompressible Navier-Stokes equations. Despite of all the advances achieved in numerical analysis in the last decades, the simulation of large-scale, real-time and parametric problems remain a challenge, especially in the Computational Fluid Dynamics (CFD) context. This can be associated to several aspects such as the solution of large algebraic systems, the governing equations nonlinearities and numerical instabilities, computational limitations, among others. This work focuses on providing low cost solution for incompressible flows with low Reynolds numbers by means of a PGD reduced basis built under a space-time decomposition employing a mixed-stabilized approach for two-dimensional flows. The methodology is evaluated with a set of numerical examples, confirming its robustness and precision, as well as a reduction in the number of linear systems to be solved and the run time compared to the standard stabilized finite element approach.