League One Posh forged into a 2-0 lead three minutes after the break but goals from substitutes Shayon Harrison and Ismail Azzaoui levelled it up going unto the final 10 minutes.
There were chances at both ends after that but Posh took the victory when Kyle Vassell struck low into the corner with five minutes left.
Only two players were aged over 20 in our squad - Kenny McEvoy, back at the club where he spent time on loan last season and captain Grant Hall, 23 - whereas Posh fielded the likes of ex-Spur Ben Alnwick in goal, former West Ham midfielder Jack Collison and highly-rated striker Connor Washington in their starting line-up.
It mattered little as the team showed maturity on the ball with a stand-out performance from Cy Goddard up against the snap and experience of Michael Bostwick and Collison in central midfield and young Academy striker Kaziah Sterling, just 16, who wasn't fazed up against a giant central defensive pair in Ricardo Almeidwa Santos and Gabriel Zakuani, a DR Congo international.
Both teams had decent efforts inside the opening minutes as Bostwick flashed wide from 20 yards before Emmanuel Sonupe and then Filip Lesniak had goalbound efforts blocked.
Hall threw himself in to deny Joe Gormley from close range and Jon Taylor sliced wide from the edge of the box.
Goddard provided our best moment of the half when he flighted a 25-yard free-kick over the wall from the left channel only for Alnwick to touch over. McEvoy then dragged wide after cutting in from the right.
Marcus Maddison zipped an effort over before Posh opened the scoring on 26 minutes. Michael Smith crossed low from the right and Gormley was there to sweep home from 10 yards.
Maddison tried his luck twice before the break, both saved by Tom Glover, the second a curler from 22 yards that the young keeper gathered well low down to his right. Glover didn't put a glove wrong in his 80-minute stint.
Newly-crowned FIFA World Under-20 champion Milos Veljkovic entered the fray in the second half alongside Christian Maghoma, Luke Amos, Azzaoui and Harrison.
Posh quickly extended their lead though as Washington drove into the box from the right, cut across Maghoma and slid under the advancing Glover.
The lads worked their way back into the game from there. McEvoy forced Alnwick to clear with his feet on 50 minutes and nine minutes later, Harrison struck. Amos got on the ball in the inside right channel, opted to come inside to Harrison rather than go wide to McEvoy and it paid off as the young striker fired low beyond Alnwick.
Posh made 10 changes just after the hour mark and we continued to push for the equaliser. Azzaoui dragged wide from a decent position and Goddard forced another save from a free-kick, this time Dion-Curtis Henry flying to his right to keep him at bay.
It wasn't long before we were at parity though as Azzaoui robbed Brad Maslen-Jones on the left byline, opened the angle by chopping back onto his right foot and lashed home for 2-2.
You fancied us to go on and win from there but Posh hit back again with what turned out to be the knockout blow on 85 minutes as Vassell found a yard of space from the right angle and shot home low off the far post.
Peterborough United - 0-60 mins: Alnwick, Smith, Ntihe, Collison (J Anderson, 36), Santos, Zakuani, Taylor, Bostwick (C), Gormley, Washington, Maddison.
Peterborough United - 60-90mins: Henry, Brisley, Maslen-Jones, Newell, J Anderson, H Anderson, Vassell, Adebayo-Rowling, plus three trialists.
Spurs XI: Glover (Sheldrick, 79); Walkes, Ball (Maghoma, 46), Hall (C) (Paul, 68), Ogilvie; Lesniak (Amos, 46), Goddard, Miller (Veljkovic, 46); Sonupe (Azzaoui, 46), Sterling (Harrison, 46), McEvoy.