This paper reports a convenient one-pot method integrating a novel solvent-exchange method into in situ melt polycondensation to fabricate unsaturated polyester nanocomposites containing functionalized graphene sheets (FGS). A novel solvent-exchange method was first developed to prepare graphene oxide/ethylene glycol (GO/EG) dispersions in a reactor equipped with a fractionating device. The prepared dispersions were applied successively to fabricate unsaturated polyester composites via in situ melt polycondensation in the same reactor. The dispersion behavior of GO/EG dispersions was characterized by atomic force microscopy (AFM). The structures and properties of the as-prepared FGS/polyester nanocomposites were characterized by Fourier transform infrared spectroscopy (FT-IR), X-ray diffraction (XRD), Raman spectroscopy, scanning electron microscopy (SEM), transmission electron microscopy (TEM), tensile tests, thermogravimetric analysis, and dynamic mechanical analysis. The results of AFM show that GO nanosheets are well exfoliated in EG solvent. The results of FT-IR, XRD, Raman, SEM, and TEM indicate that the FGS are also finely exfoliated in the polyester matrix and have strong interaction with the host polymer. Compared with the neat UPR matrix, the composite with an extremely low content of 0.08 wt% FGS exhibits maximum increases of 53.6% and 48.4% in tensile strength and modulus; the composite with 0.32 wt% FGS has a 10.7 °C increase in thermal decomposition temperature and a 17.9 °C increase in glass transition temperature. Therefore, building on this work to generate unsaturated polyester nanocomposites with improved properties at reduced cost is possible.