The 48-year-old world champion defeated Carter once more following their heated Masters final in January, when O’Sullivan won his eighth championship.
He’ll take either Zhang Anda or Gary Wilson in the Thursday 4–4 tiebreaker match.
In Manchester, Ding Junhui leads Mark Allen 5-3 overnight.
The winner of the match will play either Mark Williams or Judd Trump in their quarterfinal match on Thursday.
Seven-time world champion O’Sullivan remained silent about Carter before their most recent match, calling him “not a nice person” and “a nightmare” to play against.
However, following his decisive win on Wednesday, O’Sullivan talked candidly about a trying time that led him to consult with well-known psychiatrist Steve Peters.