The spatial discretization of the unsteady incompressible Navier-Stokes equationsis stated as a system of Differential Algebraic Equations (DAEs), corresponding tothe conservation of momentum equation plus the constraint due to the incompressibilitycondition. Runge-Kutta methods applied to the solution of the resulting index-2 DAEsystem are analyzed, allowing a critical comparison in terms of accuracy of semi-implicitand fully implicit Runge-Kutta methods. Numerical examples, considering a discontinuousGalerkin Interior Penalty Method with piecewise solenoidal approximations, demonstratethe applicability of the approach, and compare its performance with classical methods forincompressible flows.