Stewart Maxwell' s side got off to the perfect start against their East of Scotland Premier Division opponents when skipper Scott Walker gave them the lead from the penalty spot after just eight minutes.
Rabs could have added to their lead before half-time. Luke Kelly hit the post and saw another effort go just wide and Kerr McCormick's free-kick brought out a good save from the Camelon keeper.
But it remained just 1-0 at half-time and in the second half goals from Michael Wallace and Mitchell Taylor in a five-minute spell put the Carmuirs Park side through to the next round.
Boss Maxwell admitted his side paid the price for not killing Camelon off when they had the chance.
He said: "We could have been four up at half-time, but that's been the story of our season at times - we played some good football, create some chances, didn't take them
"It was a classic cup tie case of not putting a team away, and then in a crazy five-minute spell we lost two goals.
"After that we abandoned what we were doing to punt the ball long and we couldn't score.
"We went into panic mode because we were so dominant if we had got a second goal it probably would have ended up three or four.
"Th players were hurting but I said to them at the end of the game it was on them, they were slack in front of goal and had a crazy five minutes of defending so they have learned the hard way."