I knew the day before he had won.... - A little strange
before today? or before he won?
But, yes, past. Two clues, "knew" and "had".
I know the day before he have won...Your suspicion is correct - this one does not work.
"before" sort of says something "before", already past.
I can predict lottery wons. I know the day before they happen to friends. - seems sort of continuous, present.