Dimitar Berbatov handed us the dream start in Sunday's quarter-final and following Frank Lampard's equaliser, an own goal from Michael Essien and Hossam Ghaly's solo effort put us firmly in the driving seat at the break.
Crucially, Petr Cech saved one-on-one from Aaron Lennon with the score still at 3-1 and Chelsea then hauled themselves back in via Lampard again and then Kalou's heartbreaker on 86 minutes.
We still had time to strike the crossbar through Jermain Defoe but we'll have to do it all again at the Lane.
After a cagey opening few minutes the encounter sprang into life with five minutes on the clock when Jermain Defoe embarked on a mazy infield run. He prodded the ball towards Aaron Lennon, who flicked on into the path of Berbatov and the striker held off his marker to smash past Petr Cech.
Cue an eruption of noise at the Shed End of the ground - exclusively populated by Spurs people. At that same end an Essien header from a Lampard free-kick came close to causing a degree of concern, where Radek Cerny was deputising for the injured Paul Robinson.
The lead should probably have been doubled on 13 minutes when the persistence of Paul Stalteri led to Berbatov being given the freedom of the right flank. With Defoe lurking in the middle the Bulgarian crossed early, but just beyond the reach of the little hitman.
Chelsea drew level in fortunate circumstances after 21 minutes. A headed clearance from a Didier Drogba cross fell to Michael Ballack the German drilled in a shot that was heading well wide until Lampard stuck out a toe and the ball was diverted past a stranded Cerny.
The boys kept plugging away, did not lose their focus and were rewarded on 28 minutes when Teemu Tainio picked out Ghaly, who in turn provided Lennon down the right. Lennon's low centre proved too tempting for Essien not to get involved and the makeshift central defender prodded past Cech to make it 2-1.
An Arjen Robben run and cross caused big confusion moments later and Stalteri was forced to clear just in front of the line after skipper Michael Dawson and Cerny collided.
The goal joy was then trebled to the astonishment of the home supporters on 35 minutes. Ghaly set off on a run and kept going and going before bundling through a challenge outside the area and proceeding to slot the ball beyond Cech. There was probably a fair bit of pinching going on among those in our travelling army.
Essien could and probably should have got one back when a Robben free-kick clipped the top of Dawson's head and moved into the flight path of the Ghana international, who headed wide of the near post.
We got to half-time pondering the possibility of a famous victory, while always mindful of how quickly events can turn.
Chelsea were quick out of the blocks in the second period with two early Drogba chances doing much to suggest that the second half was not going to be relaxing viewing.
It would have been easier on the eye if a golden opportunity had been seized six minutes into the half. Berbatov played Lennon through on goal, Cech saved, before Ghaly chipped to the far post where Defoe was waiting to head, but the goalkeeper managed to palm the ball away. It was an afternoon of high drama.
The home side kept pressing, with us always looking dangerous on the break. Jose Mourinho loaded up on attacking players with the introduction of Kalou, while Martin bought on Mido, probably bearing in mind the amount of set pieces that were being conceded.
It was from a corner that Chelsea reduced the deficit on 71 minutes. Ballack headed downwards and the ball ran loose from the leg of Drogba and fell kindly for Lampard to drill into the net.
Didier Zokora forced a scrambling save from Cech before Steed Malbranque entered play in place of Lennon. Essien drove inches wide with ten minutes left on the clock, just before our final change of the afternoon was made with Anthony Gardner coming on for Ghaly.
It was seat of the pants stuff and resistance was broken with four minutes left when Drogba headed back across goal and Kalou volleyed past a motionless Cerny to bring the scores level.
We still had one final dart at victory when Defoe held off Lmapard to rattle the crossbar before Shevchenko drove the final effort of note just wide.
Chelsea: Cech, Ferreira (Wright-Phillips, 34), Cole (Boulahrouz, 57), Essien, Carvalho, Diarra (Kalou, 64), Lampard, Ballack, Robben, Shevchenko, Drogba. Subs: Cudicini, Bridge.
Spurs: Cerny, Stalteri, YP Lee, Dawson, Rocha, Ghaly (Gardner, 81), Tainio, Zokora, Lennon (Malbranque, 78), Defoe, Berbatov (Mido, 66). Subs: Burch, Huddlestone
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Salomon Kalou's late equaliser denied us a famous FA Cup win against Chelsea after we'd forged a 3-1 lead at Stamford Bridge.