The Yellamen fell behind to a 25th minute goal from Witney after a defensive mistake.
But Jon Bennett levelled things up from the penalty spot after 28 minutes before Lee Boon made it 2-1 five minutes into the second half with a well-placed shot into the top corner.
Ascot sealed the victory on 78 minutes from the best move of the match.
Boon fed full back Harry Holloway-Pratt and his pin point cross was met by the head of Bennett to score with a bullet finish.
It would have been four and Bennett's hat-trick but for a brilliant save from the Witney keeper from a free kick awarded after a red card offence on Ollie Lawson, which reduced the home team to 10 players.
The result puts the Yellamen into the semi-finals where they will travel to Abingdon Town.