I think by 1936 FDR won the majority of the black vote—mostly residents of Northern cities, because the blacks living in Democrat-controlled Southern states were largely disfranchised until the 1960s. Southern blacks moving to Northern cities in the early 20th century faced some of the same problems (maybe more severely) as foreign immigrants did and supported the Democrats for the same reasons the immigrants tended to.
But there was still a seismic shift in black voting patters starting in the mid 1960s. I looked this up myself years ago. I think by 1977, it culminated in a heavy favoritism for the Democrat party.
Dewey competed for black support in 1948 but still fell short.