Steve Morison scored twice to fire the visitors into a two-goal lead before the half-hour mark.
However, Charlton's top goalscorer Dean Burton hauled his side back into the game courtesy of two penalties, the latter of which saw Millwall striker Jimmy Abdou red-carded.
Nicky Bailey gave Charlton the lead two minutes into the second half before a dramatic finale at the Valley.
Dave Martin levelled nine minutes from time, slotting into the bottom left corner from six yards but Millwall appeared to have shot themselves in the foot four minutes later when Morison headed into his own net.
However, Schofield's close-range goal rescued a point for the Lions.