Bill Tate was 13-13-2 when he beat Sam Langford for the colored heavyweight championship, though he probably had quite a few undocumented fights.
Not major titles, but Jorge Kahwagi won a bunch of minor titles (WBO, WBC), and I'm not sure any of his matches weren't fixed. Really not sure that guy could win a fight without some special outside circumstances.
Manny Melchor JUST falls short. He was 19-15-4 (5) going into his title winning bout, would end his career 38-35-6 (6). But certainly deserves a mention.