Jeremie Aliadiere smashed home in extra time to finally break Spurs' resistance and help fire Arsenal to a Carling Cup final place against rivals Chelsea.
Aliadiere salutes Arsenal's crucial second at the Emirates
The Gunners dominated a lively tie and took the lead when Emmanuel Adebayor slipped in Tomas Rosicky's pass neatly.
Spurs sent the game into extra time against the odds when Mido headed in.
But Arsenal sealed a 5-3 aggregate win when Aliadiere got onto Ricardo Rocha's slip and Pascal Chimbonda's unfortunate own goal ruined Spurs' comeback hopes.
It was a remarkable end to an absorbing encounter as the Gunners denied Spurs' attempts at a smash-and-grab victory to reach their first League Cup final under Arsene Wenger.
Things got off to an ominous start for the visitors when news fed through that Aaron Lennon had been dropped after suffering through illness all day.
But any suggestion that his omission might upset the visitors was dispelled early on as they started the affair in vigorous fashion, enjoying the early possession and zipping into tackles.
One such challenge saw Phillipe Senderos leave the field to have stitches in a head wound and Arsenal's rearguard were opened up for the first time minutes later, Jenas sending Keane clear on goal, only for the Irishman's tame finish to be saved by Almunia.
However, if Tottenham needed any reminding of Arsenal's threat after the first leg, it came on 15 minutes, Paul Robinson spilling Denilson's 20-yard shot and Kolo Toure somehow screwing wide with the goal gaping.
Ironically, that seemed to settle the hosts' nerves and, with Theo Walcott to the fore, they began to carve open the Spurs defence.
The young England international should have set Adebayor up for a simple finish when he broke free down the right but failed to beat the first defender, and then his fine free-kick forced Anthony Gardner into a desperate clearance with Abou Diaby looming.
Spurs' defence was holding together adequately in the face of continued Arsenal pressure, but, after Aliadiere had fired across goal and wide on the turn, Diaby and Adebayor went close with long-range efforts that flew over.
Steed Malbranque went close with a diving header from Hossam Ghaly's cross for Spurs, and the game entered half time with the score, and match, even.
An ugly flare-up between Ghaly and Diaby ensured the second half got off to a fiery start but, despite an increase in tempo from both sides, it was Arsenal that continued to dominate possession.
Adebayor slots in the opener to give Arsenal the lead
Walcott caused all sorts of problems with no end product down the right before his withdrawal, while Denilson came close to breaking the deadlock when he cut in from the left and hit the side netting from 18 yards.
And, finally, with just 13 minutes left on the clock, Arsenal broke the deadlock when Adebayor raced onto Rosicky's pass to clip past Paul Robinson and into the corner.
However, with the game looking certain to end in Arsenal's favour, substitute Mido sent the visiting fans into raptures when he expertly guided home Jermaine Jenas's pin-point free-kick into the roof of the net - the visitors first attempt on target of the night.
Suddenly the game was up for grabs and it exploded into life, Mido tip-toeing into the Arsenal box and curling agonisingly wide, while Denilson and Toure both had stinging efforts brilliantly palmed away by Paul Robinson.
Arsenal picked up where they left off in extra-time, though, with the outstanding Michael Dawson having to do his utmost to keep Spurs in the tie.
But the centre-half could do nothing to prevent Arsenal's second as Aliadiere latched onto a slip from Rocha to blast into the corner at the end of the first extra period.
And Rosicky helped wrap up a deserved win when his superb run and shot bounced off the post and in-off Chimbonda seven minutes from time.
Arsenal: Almunia, Hoyte, Toure, Senderos, Traore (Clichy 63), Walcott (Rosicky 63), Denilson, Silva, Diaby (Fabregas 79), Aliadiere, Adebayor.
Subs Not Used: Poom, Flamini.
Booked: Denilson, Diaby.
Goals: Adebayor 77, Aliadiere 105, Chimbonda 113 og.
Tottenham: Robinson, Chimbonda, Gardner (Rocha 73), Dawson, Assou-Ekotto, Ghaly (Huddlestone 80), Jenas, Zokora, Malbranque (Mido 80), Defoe, Keane.
Subs Not Used: Cerny, Lennon.
Booked: Jenas, Gardner, Ghaly, Zokora, Defoe.
Goals: Mido 85.
Ref: A Wiley (Staffordshire).