Kyle that Census link is for Zip Code Tabulated Areas(ZCTA's) not for the actual zip codes.
It is available in the ESRI Data & Maps, you can also download from Census here: ftp://ftp2.census.gov/geo/tiger/TIGER2013/ZCTA5/
We're currently working on a ZIP Code boundary shapefile product, it's going through legal processes now, I'm not sure when it'll be available though.
One issue you'll have with ZIP polys is that they always follow feature lines, like roads. Often both sides of a road are delivered by the same ZIP, and parcels adjacent to them on one side will be another ZIP.
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