Spurs knew a point would likely secure a top-eight berth and help them avoid next month's play-off phase, but Postecoglou watched two unlikely figures come off the bench and earn a precious three points.
Dane Scarlett, 20, only returned to the club earlier this month from a mixed loan spell at Oxford but scored four minutes after his second-half introduction with a fine header for his first Tottenham goal on his 18th appearance.
Dane Scarlett scored from this fine header to help lift Spurs past Elfsborg in the Europa League. (AP PHOTO)
Damola Ajayi, a regular for the Under-21s, followed it up with a superb second six minutes from time before Mikey Moore grabbed a brilliant third in stoppage time to clinch fourth spot in the league phase for Postecoglou's men.
It was not a completely positive night for Spurs, however, as while Micky van de Ven's comeback passed by without note, fellow centre-back Radu Dragusin was forced off.
But Postecoglou toasted a memorable occasion for the club's youth set-up, saying: "It was 'Made in Tottenham' tonight. It's brilliant for the club and I'm sure there are academy coaches and players who won't sleep because they are pretty excited.
"We've got a big week coming up and we've got to try to manage the load of our players and try to protect them.
"We kind of knew we would have to rely on some young players tonight and all the way through this campaign to be honest. I thought they stood up really well.
"The whole group played well but we were going to need some young boys to make an impact and not just the three goalscorers.
"We had a couple of 18-year-olds in there as well who continue to drive us on. So it's a great night for the club and something the whole academy should be proud of."
Spurs were without 11 players for this clash and Dragusin became the latest concern after he hurt his knee when he landed awkwardly in the 61st minute.
Dragusin had come on at half-time for Van de Ven, who got through 45 minutes on his first appearance since a hamstring injury on December 8, but while the Dutch defender will be primed for more action on Sunday at Brentford, Postecoglou could be another player down.
"Unfortunately Radu's hurt his knee now," Postecoglou said.
"I don't have any further information but it didn't look good as he was coming off so we'll just have to wait and see, but it's disappointing.
"Micky got through it fine, it was always going to be 45 and he felt fine."
Fourth spot in the league phase at least means Tottenham can resume their Europa League campaign in March.
One of Real Sociedad, Galatasaray, AZ Alkmaar or FC Midtjylland will be Spurs' last-16 opponents, but Postecoglou was just pleased to avoid the play-off round and the prospect of two extra games next month.
He added: "We are through to the round of 16 and have missed the play-off game, which gives us a couple of more weeks to get players back.
"Hopefully by the time the knock-out rounds come we will have some more fit bodies to help the group and it is an exciting challenge for us."
