The north London side raced into the lead through Dimitar Berbatov, before Frank Lampard scuffed home an equaliser.
Spurs then raced into a two-goal lead through an own goal by Michael Essien and then Hossam Ghaly blasted Spurs into dreamland with their third.
But Chelsea fought back manfully and Lampard's second set up a grandstand finish for Kalou to come off the bench to send the tie to a replay at White Hart lane on March 19.
Chelsea started sluggishly and went behind on five minutes when Jermain Defoe ran direct into the heart of the Chelsea rearguard, before sliding the ball to Lennon who passed the ball on to Berbatov, who in turn smashed the ball home passed a prone Petr Cech from eight yards out.
Essien almost restored parity on ten minutes when he met another Lampard free-kick with his head but the ball sliced over the Spurs bar.
But Chelsea's talisman Lampard proved his worth once again by snatching the equaliser on 22 minute. Didier Drogba held the ball up on the left of Spurs area before sending across a clipped left-footer.
The ball was chested on by Andriy Shevchenko to the in-running Michael Ballack. His left-foot shot was deflected into the net by the right foot of Lampard from the six-yard line.
But it was Spurs who retook the lead on 29 minutes, when Lennon raced into the Chelsea area. He sent in a low drive, which Essien stretched to intercept. Unfortunately for the makeshift centre-back, he only managed to deflect the ball past Cech into his own net.
The second equaliser almost came on 32 minutes when Arjen Robben outpaced the Spurs defence and sent in a low cross which Michael Dawson flicked towards his own goal. But this time Paul Stalteri cleared the ball off the line.
Jose Mourinho decided to sacrifice his right-back Paulo Ferreira for Shaun Wright-Phillips on 32 minutes.
But within seconds Spurs netted their third when Ghaly broke through Chelsea's centre-back area and slotted coolly the ball under the body of Cech from just inside the penalty area.
Mourinho replaced both full-backs to bolster the attack. While Martin Jol brought on striker Mido to attack Chelsea's three-man defence.
Lampard pulled Chelsea back into contention on 71 minutes when he tucked home a loose ball from six yards after good wing play by Robben.
With four minutes to go Ricardo Carvalho lofted the ball to Drogba who headed into the path of Kalou, who rammed home the equaliser with a rasping volley from six yards out past Radek Cerny.
Spurs almost got a fourth when Defoe wriggled free and blasted the ball onto the Chelsea crossbar on 87 minutes.
Shevchenko's long run and shot went just inches over the Spurs crossbar and this pulsating cup-tie fell foul to the final whistle and a replay on Monday week.