We conduct X-ray spectral fits on 184 likely counterparts to Fermi-LAT 3FGL unassociated sources. Characterization and classification of these sources allows for more complete population studies of the high-energy sky. Most of these X-ray spectra are well fit by an absorbed power law model, as expected for a population dominated by blazars and pulsars. A small subset of 7 X-ray sources have spectra unlike the power law expected from a blazar or pulsar and may be linked to coincident stars or background emission. We develop a multiwavelength machine learning classifier to categorize unassociated sources into pulsars and blazars using gamma- and X-ray observations. Training a random forest procedure with known pulsars and blazars, we achieve a cross-validated classification accuracy of 98.6%. Applying the random forest routine to the unassociated sources returned 126 likely blazar candidates (defined as P_bzr_>90%) and 5 likely pulsar candidates (P_bzr_<10%). Our new X-ray spectral analysis does not drastically alter the random forest classifications of these sources compared to previous works, but it builds a more robust classification scheme and highlights the importance of X-ray spectral fitting. Our procedure can be further expanded with UV, visual, or radio spectral parameters or by measuring flux variability.