Trailing 3-1 and then 4-2 with eight minutes left, Andros Townsend scored twice in quick succession to level it at 4-4 in the 88th minute.
Both teams went for the win and the visitors found the telling strike when Jake Clarke-Salter fired home in the fourth minute of injury time.
The late flurry of goals was the second of a match that actually started slowly but exploded into life when Chelsea took the lead on 18 minutes.
Tom Glover's clearance was cut out by Reece Mitchell, who sped into the box before cutting back for Tammy Abraham to tuck away from close range.
We were soon back on level terms via a wonderful header from Shaq Coulthirst. Anthony Georgiou crossed from the left and the striker managed to generate enough power from just inside the area to loop his effort over Bradley Collins into the top corner.
Parity was short lived, however, as Chelsea were back in front two minutes later. Clarke-Salter nodded Charlie Colkett's corner back across goal for Fikayo Tomori to plant home his header from six yards.
Townsend was inches away from levelling again on 26 minutes when his low free-kick zipped just wide and as play switched from end to end, Abraham almost broke clear, Coulthirst had another shot blocked and Will Miller connected with Townsend's cross, only to see the ball deflected just past the upright. Coulthirst went close again before the break after good work centrally from Harry Winks.
Chelsea took the game by the scruff of the neck to forge two goals clear two minutes after the restart as Abraham got away down the right and picked out Kasey Palmer, who found the bottom corner from 16 yards.
Once again, we worked our way back into the match. Emmanuel Sonupe replaced Filip Lesniak on 58 minutes and wasn't far away from Townsend's cross eight minutes later while Coulthirst failed to connect with a spectacular overhead attempt.
Our reward for that pressure arrived on 72 minutes when Milos Veljkovic stepped up from the back and picked out Coulthirst who took the pass in his stride before crashing past Collins for 3-2.
Joe Pritchard replaced Anton Walkes on 74 minutes and - just like last week at United when he scored with his first touch - almost had an instant impact, inches away from connecting with Sonupe's cross.
Sonupe then forced two saves from Collins in as many minutes. First he drilled in low from 20 yards, Collins spilled and Tomori just beat hat-trick seeking Coulthirst to the rebound. Sonupe then beat Fankaty Dabo down the left before firing in to the near post, Collins this time palming away.
Chelsea remained a threat on the break, Abraham drilled straight at Glover and Colkett went close before Jay DaSilva restored the two-goal advantage by curling home from the edge of the box for 4-2 on 82 minutes.
It wasn't time to throw in the towel though and when our final substitute, Cy Goddard, was upended by Tomori, Townsend stepped up to bury the penalty for 4-3, 85 minutes on the clock.
Goddard then turned provider again, this time escaping a wild challenge on halfway before finding Coulthirst, who then released Townsend. The winger did the rest, shifting right of DaSilva before drilling home for 4-4.
With the way the game had unfolded, there simply had to be winner. We almost broke through again on 92 minutes but play switched back again and Glover was forced into a one-on-one save from Abraham.
Unfortunately, the final, decisive, action went Chelsea's way in the 94th minute. Dabo floated in a free-kick that we failed to clear and Clarke-Salter fired low across Glover into the far corner for 5-4.
Spurs U21s: Glover, Amos, Georgiou, Lesniak (Sonupe 58), Veljkovic (c), Carter-Vickers, Townsend, Winks, Coulthirst, Walkes (J Pritchard 74), Miller (Goddard 83). Substitute (not used): Voss (GK).
Chelsea U21s: Collins, Dabo, Tomori, Clarke-Salter, DaSilva, Colkett (c), Mitchell, Ali (Kiwomya 46), Abraham, Palmer, Musonda. Substitutes (not used): Wright, Quintero, Colley, Russell (GK).