Studies of the diffuse x-ray-emitting gas in galaxy clusters have provided powerful constraints on cosmological parameters and insights into plasma astrophysics. However, measurements of the faint cluster outskirts have become possible only recently. Using data from the Suzaku x-ray telescope, we determined an accurate, spatially resolved census of the gas, metals, and dark matter out to the edge of the Perseus Cluster. Contrary to previous results, our measurements of the cluster baryon fraction are consistent with the expected universal value at half of the virial radius. The apparent baryon fraction exceeds the cosmic mean at larger radii, suggesting a clumpy distribution of the gas, which is important for understanding the ongoing growth of clusters from the surrounding cosmic web.