The fourth Fermi Large Area Telescope catalog (4FGL) contains 5064 {gamma}-ray sources detected at high significance, but 26% of them still lack associations at other wavelengths. The SPT-SZ survey, conducted between 2008 and 2011 with the South Pole Telescope (SPT), covers 2500deg^2^ of the southern sky in three millimeter-wavelength (mm) bands and was used to construct a catalog of nearly 5000 emissive sources. In this study, we introduce a new cross-matching scheme to search for multiwavelength counterparts of extragalactic {gamma}-ray sources using a mm catalog. We apply a Poissonian probability to evaluate the rate of spurious false associations and compare the multiwavelength associations from the radio, mm, near-infrared, and X-ray with 4FGL {gamma}-ray sources. In the SPT-SZ survey field, 85% of 4FGL sources are associated with mm counterparts. These mm sources include 94% of previously associated 4FGL sources and 56% of previously unassociated 4FGL sources. The latter group contains 40 4FGL sources for which SPT has provided the first identified counterparts. Nearly all of the SPT-associated 4FGL sources can be described as flat-spectrum radio quasars or blazars. We find that the mm band is the most efficient wavelength for detecting {gamma}-ray blazars when considering both completeness and purity. We also demonstrate that the mm band correlates better to the {gamma}-ray band than the radio or X-ray bands. With the next generation of CMB experiments, this technique can be extended to greater sensitivities and more sky area to further complete the identifications of the remaining unknown {gamma}-ray blazars.