Denis Shapovalov was in disbelief while captain Frank Dancevic admitted he almost blacked out as Canada advanced to the Davis Cup final for the first time.
The 20-year-old Shapovalov teamed up with Vasek Pospisil to win the deciding doubles rubber against Russia's Andrey Rublev and Karen Khachanov and seal a 2-1 victory for Canada.
They will play hosts Spain in Sunday's decider after a gripping second semi-final.
Britain’s Kyle Edmunds beat Feliciano Lopez 6-3 7-6, before Spanish superstar Rafael Nadal downed Dan Evans 6-4 6-0 to set up a deciding doubles rubber.
However, it was Nadal and Lopez that partnered up in the doubles to take down British pair Jamie Murray and Neal Skupski.
The Spaniards took out a tense first set in a tiebreaker and the next set followed the same script as the first.
Even more drama ensued in the second set tiebreak but again it was Spain that prevailed - booking their spot in the decider against Canada with a 7-6(3) 7-6(8) victory.
For Canada and Shapovalov, particularly, the semi-final win was especially sweet as the Davis Cup has not always been kind to him.
In 2017, in his second tie, he was defaulted from a World Group tie against Britain after accidentally striking the umpire with a ball.
That was all forgotten though as he and Pospisil, ranked 150th after missing six months this year because of back surgery, held their nerve after the tie boiled down to a third-set tiebreak.
After winning 6-3 3-6 7-6 (7-5) the two danced for joy as several hundred Canadian fans roared their approval.
“I have no words, it’s unbelievable,” the 20-year-old Shapovalov said on court as Canada’s fans celebrated.
"I don't think any of us expected that we could get this far."
"We knew we have a great team but you have to have a little bit of luck on your side and just play some ridiculous tennis and play at a ridiculous level.
"I think we just absolutely played ridiculous tennis.
"I'm super-stoked to be in the final. It's one of my dreams, you know, to play in the Davis Cup final."
With Milos Raonic injured and another of Canada's young guns, world No.21 Felix Auger-Aliassime, unable to play a match so far this week, Dancevic has had to rely on a two-man team.
Pospisil lost 6-4 6-4 to Rublev on Saturday but left-hander Shapovalov, whose parents are Russian, stepped up to level the tie, showing great tenacity to beat Khachanov 6-4 4-6 6-4.
After the latest thrilling tie at the revamped Davis Cup, Dancevic said it had been hard to sit on the chair and watch.
"When I was sitting there on match point, my heart was beating so fast, I was actually starting to black out," he said.
"I was trying to control my breathing and just telling myself to breath slowly, stay calm... at the day it's an amazing feeling having your guys perform like this and put 110 per cent on the court."
Meanwhile, Rafael Nadal made it 27 Davis Cup singles wins in a row to draw Spain level with Great Britain and send their tie to a decisive doubles rubber.
The world No.1 saw off Dan Evans 6-4 6-0 after Kyle Edmund gave Britain the perfect start by beating Feliciano Lopez - a very late substitute for Pablo Carreno Busta - 6-3 7-6 (7-3).
Nadal and Lopez will team up to take on Jamie Murray and Neal Skupski with the winners securing a spot in the final against the Canadians.