The game at the Johan Cruijff ArenA end in a 3-2 victory for Spurs, but the North London club found themselves down two goals in the first half.
Spurs boss Mauricio Pochettino saw his players rally in the second half and a superb hat-trick performance from Lucas Moura took the game to 3-3 on aggregate with Tottenham winning the tie on away goals.
Financial restrictions at Tottenham has prevented Pochettino from signing any players in the last two transfer windows and the last player he brought into the club was Moura.
The deal in the 2018 January transfer window saw the Brazilian move from Paris Saint-Germain for £25million and the French club’s manager at the time was Emery.
The 26-year-old was part of Emery’s squad for 19 months but found playing time limited as he only made seven appearances before being moved on by the Spaniard.
Injury limited Moura’s appearances for Spurs in his debut season but he has been a useful option for Pochettino this campaign.
Spurs came into the game in Amsterdam trailing 1-0 from the first leg and didn’t get off to the best of starts when Ajax’s captain Matthijs de Ligt scored after just five minutes.
Ajax winger Hakim Ziyech then extended the Dutch team’s lead with a fabulous first-time strike from a pass from ex-Southampton playmaker Dusan Tadic.
However, the second half belonged to Moura. He wasted no time getting Tottenham back into the game with a goal five minutes after the restart.
He then added his second of the night with a shot on the turn to beat Ajax’s keeper Andre Onana in the 59th minute.
The stage was then set for another dramatic Champions League comeback and Moura didn’t disappoint and his determination rewarded him with an opportunity in the 95th minute.
Dele Alli laid off a pass to Moura on the edge of the box who then cooly slotted the ball home into the bottom right corner and in the process sent Tottenham to the Champions League final in Madrid on June 1.
After the shocking victory Moura praised his team-mates for helping him.
“I don’t have words to explain this moment!” Lucas said.
“It’s very special for me, I am very, very happy and very proud of my team-mates.
“Of course, I need to share (this moment) with all my team-mates, my family, my friends.
“I always believed it was possible to come here, to win and to go to the Final.
“We fought – that’s what we needed to do with our intensity. The second half was amazing and everyone did really well.
“I need to enjoy this moment – it’s impossible to explain!”