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We propose a model for enhancing power system state estimation (SE) with synchronized phasor measurements based on a two-pass approach. The first pass consists of executing the traditional state estimation problem without the phasor measurements. The second pass appends the state vector solution with the vector of phasor measurements and solves a linear state estimation problem in rectangular variables. Our model is non-invasive in the sense that phasor measurements are not directly integrated with traditional state estimation inputs of real, reactive power and voltage magnitudes. Numerical experimentations on the New England 39 bus test system for varying number of phasor measurement units (PMUs) were conducted. Test results show the effectiveness of the proposed method of phasor integration in improving the quality of the state estimator solution.