Spurs travelled to Amsterdam having lost the first leg at their new stadium 1-0, thanks to a Donny van de Beek goal.
And they made a slow start at the Johan Cruyff ArenA as Matthijs de Ligt doubled the hosts’ advantage within five minutes.
Just before half-time, the tie looked to have been sealed as Hakim Ziyech made it three for Ajax and gave Tottenham a near-impossible ask in the second half.
But a Lucas Moura masterclass saw Spurs claw two goals back within the space of five minutes just before the hour mark, before the most dramatic of finishes.
With seconds remaining in the fifth minute of injury time, Moura sealed his hat-trick by scoring a perfectly timed effort from the edge of the area to send Spurs through on away goals.
Minutes later the full-time whistle secured Tottenham’s first-ever Champions League final, and Pochettino, his staff and substitutes poured onto the pitch.
The Argentine coach then went over to the thousands of travelling Spurs fans to show his appreciation and was caught on camera bowing down to the away supporters.
It has been a somewhat difficult year for Pochettino and Spurs, having seen their successes on the pitch marred by speculation off it surrounding the coach’s future.
Pochettino was fancied for the Manchester United job, and fans feared that they would lose their manager at the end of the year. As well as that, they were plagued with a series of delays to their new stadium and were forced to stay at Wembley.
And the head coach’s relief was clear for all to see as he appeared to wipe away tears before saluting the away faithful.
Pochettino raised eyebrows on Tuesday as he suggested that he could leave the north London club at the end of the season if Spurs win the Champions League.
“To win in these circumstances this season, maybe I need to think about maybe doing something different in the future,” he said at a press conference.
“It’s not a joke. Winning the champions league would be fantastic, no? Close the five-year chapter and go home.
“We are living a dream. Five years ago, when we arrived, [the aim] was to reduce the gap to the top four, and then to have the possibility to play in the Champions League.
“Nobody would believe we would be playing in the Champions League three seasons in a row and competing at this stage.”
Tottenham will take on Liverpool in the Champions League final at the Wanda Metropolitano stadium in Madrid on June 1.