Everything was looking rosy five minutes before half-time as the team looked to have played the perfect first half, not only keeping Chelsea at bay but adding to our first leg advantage via Shayon Harrison's fine strike.
But it all changed in the next 14 minutes as goals from Dominic Solanke (41 minutes), Isaiah Brown (45), Solanke (51) and Charlie Colkett (54) put the home team 4-1 up on the night and 4-3 up on aggregate in our two-legged semi-final.
Colkett's second from the penalty spot left us two goals adrift overall at 5-3 but we found the spirit for a late response, Harrison made it 5-4 on aggregate and both Josh Onomah and Cameron Carter-Vickers were denied aggegate equalisers in the final minutes, but it wasn't to be.
Leading 2-0 from the first leg at the Lane, the lads settled into the game well and forced the first two saves of the night from Bradley Collins.
Onomah was first to try his luck from 30 yards, Collins parried away to his left and the goalkeeper was down again within seconds to turn away Harrison's low drive from the edge of the box.
Tammy Abraham had Chelsea's first sight of goal, his effort blocked by Carter-Vickers and Harry Voss was at full stretch to claw away Jay Dasilva's cross on the half-hour.
Roared on by a healthy following of Spurs fans, the half got better for the team in white on 32 minutes with a magnificent finish from Harrison. Onomah swung in a corner, Chelsea half-cleared, Zenon Stylianides hooked the ball back in and Harrison watched the ball over his shoulder before volleying into the far corner for 1-0 on the night, 3-0 on aggregate.
As expected, that goal stung Chelsea into action. Ruben Sammut fired just wide and then Abraham and Dasilva somehow failed to convert Brown's cross in front of goal.
The home team's response arrived on 41 minutes when Solanke turned home another Brown cross from close range for 1-1 on the night, 3-1 on aggregate.
We could have restored our three-goal advantage immediately as Onomah got away down the left and his cross found Stylianides at the far post. His low shot beat Collins but Dasilva got back to clear off the line.
Chelsea took the lead on the night just before half-time as Colkett's corner was met by Jake Clarke-Salter and Brown smashed home the loose ball for 2-1 in the second leg and 3-2 to us on aggregate.
Voss was tested within 40 seconds of the restart as Abraham got away down the right and shot towards the top corner, our goalkeeper tipping over. Clarke-Salter powered his header just wide from the corner.
We were then caught in possession and Chelsea broke quickly with Abraham through centrally. He opted to turn back onto his right foot but Kyle Walker-Peters got back to steal the ball.
Chelsea didn't have to wait long to level it up on aggregate though as Brown released Ola Aina down the right and his cross was headed home by Solanke for 3-1 on the night, 3-3 on aggregate, with 51 minutes on the clock.
It was soon 4-3 overall as Colkett took Voss by surprise by whipping a free-kick directly home from the right angle for 4-1 on the night, 54 minutes gone.
We were inches away from levelling the tie on aggregate when Charlie Owens slid Stylianides' cross onto the post on 59 minutes but play switched to the other end as Voss saved well from Colkett and Aina fizzed just wide.
It was 5-1 on the night on 72 minutes when Anton Walkes tripped Aina and Colkett rolled home from the penalty spot and Chelsea then created chances, Aina deflected Dasilva's cross wide from six yards before Sammut missed the target when through on goal from Abraham's backheel.
Cy Goddard and Kazaiah Sterling entered the fray with 12 minutes remaining and the game open as we chased two goals to stay alive in the tie.
We were handed a lifeline on 82 minutes when Fikayo Tomori slid in on Harrison and handled the ball on the ground. Harrison stepped up and slotted home for 5-2 on the night, 5-4 overall.
Momentum was suddenly back with us and Clarke-Salter found a goal-saving block to deny Onomah in front of goal on 89 minutes.
We just needed that one chance and it arrived in the final seconds of five minutes added time. Goddard clipped in a free-kick, Carter-Vickers rose highest to aim a looping header to the top corner but Collins was there to touch the ball over - and our hopes ended there.
Chelsea: Collins; Aina, Tomori, Clarke-Salter, Dasilva; Sammut (Scott, 78), Colkett (c), Boga (Musonda, 72); Brown (Palmer, 90+3), Abraham, Solanke. Substitutes (not used): Thompson, Grant.
Spurs: Voss; Walker-Peters, Carter-Vickers, Maghoma, Walkes; Amos, Owens (Paul, 68); Stylianides (Goddard, 77), Onomah (c), Azzaoui (Sterling, 77), Harrison. Substitutes (not used): Edwards, Glover (GK).