The Premier League side came into the second leg of the semi-final tie 1-0 down, having suffered a disappointing home defeat last week.
And after the first half of action in Amsterdam, it appeared they were heading out of the competition with a whimper, conceding twice in the first 45 minutes of action.
However, a stunning second-half hat-trick from Lucas Moura ensured Spurs progressed to the final on away goals, with an all-English affair against Liverpool to look forward to now on June 1.
Ajax appeared to be in control of the contest for large periods, but Tottenham always looked a threat when bypassing the midfield to find Fernando Llorente up front.
Moura's decisive effort came with virtually the last kick of the game, which prompted the home side's stars to fall to the ground in disbelief.
Blind was particularly flummoxed by the result, admitting he does not know how Ajax will move forward after such a dramatic evening.
The 29-year-old told Veronica : "I don't know how to recover from this. I guess everyone has their own way, but we have to be back on track by Sunday [for their penultimate Eredivisie game against Utrecht].
"I'm glad we will be having another match soon. It hurts. Yesterday [Liverpool's win over Barcelona] we've seen that everything is possible. We told ourselves that.
"We had a great opponent with lots of qualities. We delivered a lot of passion. After the 2-2 we restored the match. Hakim [Ziyech] had two good opportunities. It's such a shame he couldn't finish it.
"This match should have lasted 10 fewer seconds. They didn't get many chances after the 2-2, but they scored anyway and that's devastating.
"I'm extremely proud to be part of this team. We've shown fantastic stuff and I think the whole world enjoyed it, but it's a bit too early for us to think like that.
"Anyway, we have to go on. We have to win another trophy with this team. We're going to make sure the season ends in a fantastic way."
Having lifted the KNVB Cup over the weekend, Erik ten Hag's side are still on course for a superb domestic double, as they sit top of the Eredivisie on goal difference ahead of PSV with two matches of the season remaining.
Tottenham, meanwhile, are chasing their first piece of silverware since 2008 and will be considered underdogs against the Reds, who overcame Spanish giants Barcelona in their semi-final by winning 4-0 at Anfield.
Spurs must turn their attention to the final day of the 2018-19 Premier League season before preparations for the final can begin, with a home clash against Everton on the cards.
Pochettino's men need at least a point to guarantee a place in the top four, with arch-rivals Arsenal behind them in fifth.