They ended Manchester City's 100 per cent home record despite having to play for 70 minutes with only ten men after Didier Zokora's controversial sending off.
But Spurs, revitalised under new manager Juande Ramos, displayed grit and determination to not only protect Jermain Defoe's early lead, but double it late on through Steed Malbranque.
It was their third successive victory in league and cup, a feat they have not previously achieved in the current campaign.
While Spurs had plenty to celebrate, it was a sad night for City who, incredibly, were bidding to reach their first domestic cup semi-final for 26 years. The defeat also ended their remarkable run of ten successive home wins in league and cup.
Spurs made a dream start, taking a fifth minute lead through Defoe, who was probably only in the side because Robbie Keane was suspended and Darren Bent injured.
Defoe finished off a neat passing move with a near post shot from Aaron Lennon's right-wing cross, his fifth goal of the season.
But Spurs looked to be facing an uphill struggle when Zokora was dismissed in the 20th minute following a challenge on Elano which referee Steve Bennett deemed to be two-footed to the amazement of everyone in the ground.
Ramos was forced to substitute goalscorer Defoe, much to his displeasure, as Teemu Tainio was brought on as their defence had to be rejigged.
Spurs lost their discipline and were lucky not to be reduced to nine men not long after when Malbranque scythed down Javier Garrido in what was a far worse foul than the sending off offence.
City struggled to make a breakthrough against Spurs' well-drilled defence as the visitors got men behind the ball in great numbers every time they lost possession.
And on the few occasions they breached the back line, Paul Robinson showed why, until recently, he was England's number one keeper.
In the second half, Robinson made two breathtaking reflex saves, first to turn over a goalbound header from Darius Vassell and then later keeping out what looked a certain goal from a header by substitute Emile Mpenza.
Spurs sealed victory with seven minutes left when Malbranque broke clear on to a long forward pass from substitute Jamie O'Hara and slotted a shot low past keeper Joe Hart.