Madden fired low past George Long after being set up by Byron Webster four minutes after half-time and was then rewarded for his tenacity in the 66th minute, walking the ball into the net after catching the keeper in possession.
Glovers boss Johnson said: "I thought it was a fantastic performance. It was a colossal performance from our back players - a real clever, strong-running performance by our midfield four and our front two worked their socks off.
"Paddy's never-say-die running got us the two goals and we had chances in the first-half.
"I said at half-time that we'd go away really disappointed if we don't win this game. We felt that we had them where we wanted them.
"I don't think anyone can say that we didn't deserve that result. We came here to get on the ball and play and show that we could do something.
"We've got a group who are pretty inexperienced and we're proud of them all at the moment."