It actually doesn't. Even with the addition of the 14th amendment most states that ratified it still had laws that segregated schools on the books (including northern states). The Framers of the 14th amendment certainly did not intend it's usage to apply to desegregation. The totality of the equal protection clause guarantees due process which the laws aptly address. Therefore, though Brown V. Board is something politically with which we all agree it represents an egregious encroachment of judicial authority on the process of government similar to Dred Scott yet in a favorable ends.
