The team was faced with a 3-0 deficit after 35 minutes of the quarter-final meeting but, far from throwing in the towel, showed great heart to fight back and push our London rivals to the limit.
We looked a different team in the second half as Anton Walkes and Will Miller turned 3-0 into 3-2 but that third goal proved a bridge too far and Chelsea put the issue beyond doubt with two Tammy Abraham goals in the closing minutes.
Emmanuel Sonupe - a threat down the right - had the first chance blocked by Jake Clarke-Salter after two minutes but Chelsea were quickly in the ascendancy.
Reece Mitchell opened the scoring on six minutes with a thunderbolt that rattled home off the underside of the crossbar and that was followed by a strike of equal quality four minutes later as Kasey Palmer curled low into the bottom corner from just inside the box.
Clarke-Salter and Abraham had chances after that but we started to get a foothold in the game midway through the half as Anthony Georgiou just failed to convert Sonupe's cross.
Those shoots of recovery looked to have been flattened by Ola Aina's spectacular effort 10 minutes before half-time, though. Picking up the ball just inside his half, Aina took aim and drove at goal, his low-trajectory effort sailing like a missile over goalkeeper Tom Glover and into the net.
To their credit, the lads responded and carved out the best chances before the break as Sonupe was first denied by Bradley Collins after latching onto Milos Veljkovic's fine pass and then fired just wide from Georgiou's cross.
Whatever words were said at half-time did the trick as we looked a team inspired in the second period.
Miller and Sonupe went close within two minutes of the restart and it was no surprise - and no less than we deserved - when Anton Walkes drove into the corner via a slight deflection from 20 yards for 3-1 on 54 minutes after being set up by Kyle Walker-Peters.
Goalkeeper Glover denied Charlie Wakefield one-on-one with his outstretched boot but it was a brief respite for the visitors as Miller's free-kick deflected just wide and a huge scramble from a corner saw respective Veljkovic shots blocked twice from close range and then Collins get in the way of Walker-Peters' follow-up.
It was game on with 20 minutes remaining thanks to a fine goal. Joe Pritchard started the move with a cross-field pass to Sonupe and his cross from the right was met by Miller, who planted home a diving header for 3-2.
Nathan Oduwa returned to Under-21s action off the bench on 74 minutes after recently coming back from his loan at Rangers as we threw the dice.
But Chelsea remained a threat on the break and finished the contest on 87 minutes when Abraham turned home Fankaty Dabo's cross from close range. Abraham added his second and Chelsea's fifth in the fourth minute of added time when he advanced at Walker-Peters and steered a shot low into the corner from 15 yards.
Spurs U21s: Glover, Walker-Peters, J Pritchard (Oduwa 74), Lesniak (Goddard 63), Maghoma, Veljkovic (c), Sonupe, Amos, Miller, Walkes, Georgiou. Substitutes (not used): Paul, Voss (GK).
Chelsea U21s: Collins, Dabo (c), Aina, Clarke-Salter, Wright, Houghton (Sammut 75), Wakefield (Conroy 80), Quintero (Scott 69), Abraham, Palmer, Mitchell. Substitutes (not used): Ugbo, DaSilva, Baxter (GK).