Faithfold then battled well and scored two more in the second half to secure the points.
Oakwood's goals came through Josh Bentley and Anthony Kintish.
Faithfold boss Zuriel Solomon told JC Sport: "Today was areal battle. Overall happy with the win in difficult weather conditions. We had three drop-outs last night so only had 12 boys, but they showed some great desire.
"Oakwood are a big physical team and they will get results sooner rather than later. They miss a potent striker and when they get one I think they will be very dangerous."
Oakwood joint-manager Ric Blank told JC Sport: "DC, I'm down but not out following the result. The simple truth is we were outstanding - the better team lost. The chances we missed were criminal, but I cannot fault the application and commitment of all the players.
"We can't be too happy with ourselves because we still conceded four goals and lost - but we are on the right track. When we win one we'll go on a run and no-one will want to play us. It's now up to the boys to be available and keep themselves fit to make it happen.
"Faithfold are a really good side and though they've beaten us twice they'll be grateful they don't have to play us again. We hope to get another crack at them in the cups sooner rather than later."