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We perform an ab initio study of spin-polarized tunneling in epitaxial Co|SrTiO3|Co magnetic tunnel junctions with bcc Co(001) electrodes. We predict a large tunneling magnetoresistance in these junctions, originating from a mismatch in the majority- and minority-spin bands both in bulk bcc Co and at the Co|SrTiO3 interface. The intricate complex band structure of SrTiO3 enables efficient tunneling of the minority d electrons which causes the spin polarization of the Co|SrTiO3 interface to be negative in agreement with experimental data. Our results indicate that epitaxial Co|SrTiO3|Co magnetic tunnel junctions with bcc Co(001) electrodes are a viable alternative for device applications.