Furness trailed 4-3 to Buxton Reserves with time running out, but dug deep to win through.
Tom Scorer with a typically hard-worked goal, involving a quick turn and shot, levelled.
Then with the tie looking to be heading to extra-time, a loose ball went through to Ben Higginbottom, who kept his nerve and coolly slotted home in the 83rd minute to clinch a 5-4 win and a place in the final.
After two postponements due to bad weather, the tie was played at Rowton Park, Chapel.
Furness, beaten just once in 12 months, faced a stern test against a good Buxton side who are flying in the Cheshire League.
Both sides set up to attack, knowing that with the weather deteriorating it was important to get a good start.
Furness took advantage after early pressure, which appeared to take Buxton by surprise.
Scorer, who has been a revelation since joining the club, managed to round the keeper from a through ball and slotted in.
Buxton responded immediately with fast, attacking football and were soon level.
A set-piece undid Furness as Buxton’s number eight was left unmarked and scored on the half volley.
More end-to-end football followed with Buxton adding to their tally after a sharp move down the wing, good cross and fine finish.
Furness quicklyequalised through Mike Jodrell on the stroke of half-time.
The topsy-turvy semi-final took another twist at the start of the second half, which started as the first half had finished — with Furness scoring.
Nick Wood fired Furness in front and they continued on the front foot.
However, a heavy pitch began to take its toll on the game and the young Buxton reserve team replied with two quick-fire goals to regain the lead, first through a set-piece and then a well-driven shot from range.
Furness hit back with their two late goals to again turn the tie on its head, but Buxton fought back with late pressure. This time, however, Furness held on.