The Hammers won 3-0 in the Premier League encounter in October in one of the results which ultimately cost Andre Villas-Boas his job and saw Tim Sherwood placed in charge of Spurs for the League Cup quarter-final.
Sherwood thought he had made a dream start to life in the dugout when Emmanuel Adebayor put Spurs in front midway through the second half, but Matt Jarvis scored 10 minutes from time and Modibo Maiga headed in an 85th-minute winner to send the Hammers, struggling in the Premier League, into the semi-finals.
The Hammers, who had won just two of the 10 matches between visits to White Hart Lane, had been blunt until exposing the defensive deficiencies which were all too evident all too often during Villas-Boas' reign, including in Sunday's 5-0 home loss to Liverpool.
Hammers boss Sam Allardyce knows Premier League results will determine his future, but a place in the last four and the prospect of a Wembley final could provide a much-needed fillip for his relegation-threatened side.
It had appeared Allardyce would have more immediate worries over his position when former West Ham striker Jermain Defoe crossed for Adebayor to net a thumping volley after 67 minutes. It was his first goal since the May win at Stoke.
The strikers - in particular Adebayor, who was making his first start of the season - were marginalised by Villas-Boas and provided an emphatic answer to their former boss.
But Adebayor ran out of energy and was replaced, Andros Townsend went off with a hamstring injury and West Ham struck twice late on to advance.
With the selection of Adebayor and Defoe as two of six changes in a conventional 4-4-2 formation, Sherwood made a statement.
The former Spurs captain, wearing a tracksuit and trainers, showed more energy than Adebayor in Spurs' opening attack, imploring Aaron Lennon to sprint down the right before Defoe dragged a shot wide.
Townsend shot wide from the edge of the area before another Lennon cross caused danger in the Hammers' box and Joey O'Brien headed too close to his own post for comfort in conceding a corner.
O'Brien conceded another set-piece when Adebayor attacked the right side of the area and then the Togo striker headed a Townsend cross wide.
Defoe blasted over, much to Sherwood's frustration, as West Ham struggled to break free of their own half.
Carlton Cole shot straight at Hugo Lloris has the visitors registered an effort on target for the first time after 36 minutes.
The Hammers resumed on the defensive and registered a second shot on target in strange circumstances.
James Collins kicked the ball back to Spurs following an injury to George McCartney, but instead of a tame pass to a member of the opposition, the Wales defender booted the ball from inside his own half and forced Lloris to back-pedal to save.
From a West Ham corner, Spurs broke to devastating effect.
Townsend fed Defoe, who ran down the left before crossing to the back post where Adebayor did the rest, converting with a thunderous right-footed volley which went in off the underside of the bar. Adebayor has now scored three times in his last four Spurs starts.
Mohamed Diame, on for Joe Cole, forced Lloris to save low to his left as the Hammers sought a swift response.
Townsend pulled up worryingly for Spurs and departed with 17 minutes remaining, with Nacer Chadli on in his place.
Lloris saved a Matt Taylor effort from 25 yards before Adebayor made way with 12 minutes remaining to a rousing reception from the home faithful.
But instead of Tottenham closing out victory, West Ham equalised when Maiga flicked on goalkeeper Adrian's long ball to Taylor.
With his back to goal, Taylor turned and fed Jarvis on the left and the winger was granted enough space by Kyle Walker to fire in.
O'Brien made a fine challenge to deny Chadli after the midfielder broke into the West Ham box and shaped to shoot.
The Hammers then struck again after substitute Ravel Morrison found Diame.
Diame's deep cross was met at the far post by Maiga, whose header found the corner for his first goal in a year.
Sigurdsson was denied by Adrian in the first of five minutes of added time as the visiting fans taunted Tottenham and Sherwood, exclaiming "You're getting sacked in the morning".
Maiga then struck the crossbar with a powerful drive and Jack Collison forced Lloris to save as West Ham finished the contest on top as they sealed their progress.