Who was the last democrat to win southern whites?

[Wazza [INACTIVE]]

LBJ received 6,096,989 to Barry Goldwater's 5,993,384 in the 11 Confederate states (Obviously not including the 210,732 votes in Alabama that went to the unpledged Democratic slate). Considering that the vast majority of the voting populations in Southern states in 1964 were white, the answer is most likely (narrowly) Lyndon Johnson.

Of course we could throw the non confederate Southern states like WV, OK and KY in which case Johnson would be safely winning the Southern White vote.

[Wazza [INACTIVE]]

Huh, I didn't realise the Black electorate was that significant in the South prior to the VRA.

Eisenhower did beat Stevenson in the 11 Confederate States by 97127 votes  (4212324 to 4115215) in 1956. In 1952 however, Stevenson beat Eisenhower by 314620 votes (4428163 to 4113543). I'm not knowledgeable on the Black electorate in the South during the 50s apart from that it was under-representative and that on the national level Black voters backed Stevenson twice. Though either way the answer to OP's question would be Stevenson.