Jack Stacey scored a 95th minute winner to send Exeter to the Sky Bet League Two play-off final after they beat Carlisle 3-2 on the night and 6-5 on aggregate.
After an epic first-leg which ended 3-3, this tie somehow surpassed what went before as Carlisle once again battled back from two-goals down before Stacey, who had never scored for Exeter, struck with the last kick of the game.
The highly-rated Ollie Watkins had put Exeter 5-3 up on aggregate with a classy double but with eight minutes to go Jason Kennedy gave Carlisle hope before John O'Sullivan sensationally levelled the tie on 90 minutes, which looked to have forced extra-time.
Live League Two Play-Off Final
However, there was to be one last moment of drama as Stacey, on loan from Reading, cut in from the right wing and let rip a stunning left-foot strike that flew into the top corner.
Paul Tisdale's men will now face Blackpool at Wembley on May 28, which is live on Sky Sports.
The Grecians went in front with their first effort at goal on 10 minutes.
David Wheeler got the better of Tom Miller and laid the ball back to Ollie Watkins, whose scuffed shot took a deflection and somehow found its way past Mark Gillespie in the Carlisle goal.
Carlisle started a pulsating second half with real intent and almost equalised inside 14 seconds, but Nicky Adams' angled shot was well saved by Bobby Olejnik.
Watkins almost made it 2-0 to Exeter shortly past the hour mark when he showed great strength before turning and lashing a shot goalwards, but Gillespie got down brilliantly well to turn the ball behind and substitute Joel Grant also missed a great chance after a brilliant solo run.
With 10 minutes remaining Watkins seemed to have put the game beyond doubt.
Wheeler was again the architect, driving at the heart of the Carlisle defence and feeding the ball to Watkins, who got the ball onto his left foot and curled a beauty into the top corner from 15 yards.
But Carlisle hit back within two minutes as Exeter struggled to clear a corner and Jason Kennedy scrambled the ball over the line to give the Cumbrians hope.
In the final minute, a deep cross from Adams found John O'Sullivan and he steered a fine header into the bottom corner.
However, with almost the last kick of the match, Stacey booked Exeter's Wembley date with a sensational left-footed effort from distance.
Exeter boss Paul Tisdale
"I have been here before with Exeter, I have been in two finals, won one and lost one, so I know what it feels like to win and I know what it feels like to lose.
"It really is the best place to win and the worst place to lose.
"We have gained an opportunity now, but that is all it is. Jack Stacey scored the winning goal, but there is a big group of players that have got us this far, it is not just him.
"We had three players that started on Sunday that didn't start tonight. They weren't dropped, I just selected an XI, so there are a lot of players that have got us this far and now we have to make the very most of it.
"I said (when Exeter were bottom of the table in November) that this was the best group of players that I have had in seven or eight years and people thought I was crazy, but I believed that. I believed in the players."
Carlisle boss Keith Curle
"We walk out of the stadium with our head held high. They have given me everything, of course there is an element of disappointment.
"But what we don't do is we don't sulk out of here, we have improved since I have been at the football club and there is a winning mentality at this club that we need to maintain.
"We have enjoyed the challenges this season and we have taken a very good team all the way. They have had a manager that has been able to put foundations here for 10 years and we have given them a run for their money.
"We won't give in and I am proud of that. There will be changes at the club because there needs to be. There is a willingness to give everything, I am very proud of the players. They have done me proud. Even at 2-0 down I still thought we were going to get a goal."