The O's took the game to their opponents, sitting third in the Premier Division, and took the lead on the stroke of half time when top scorer Tom Morgan lobbed the keeper for his seventh goal of the season.
Odd Down equalised with a goal that looked suspiciously like a hand was used but new signing David Stone, on his debut, grabbed a sensational late winner to book Oldland a place in the next round where they will face a home tie with Buckland Athletic, another Premier side.