Defoe had a goal ruled out for offside but soon flicked in at the near post following a David Bentley cross.
In injury time the England striker rounded the goalkeeper to complete his treble for his 20th goal of the season.
When Spurs arrived at Elland Road snow was falling heavily and with Leeds having lost only twice in 21 matches at home this season the scent of an upset was evident.
But the Londoners quietened the hostile home crowd by applying an admirable work ethic to their superior technical ability and dominated for the vast majority of the contest.
The pitch looked heavy through the middle but was perfectly playable, and if anything suited Tottenham's slick passing style more.
Defoe might have scored in the second minute when an attempted header back to the goalkeeper from Andrew Hughes fell woefully short, but the England striker scuffed his shot.
Spurs defender Sebastien Bassong found himself in a surprising amount of space on the penalty spot from Bentley's corner but scooped over when he might have had time to have controlled first.
Defoe looked dangerous whenever the visitors went forward, he should have scored when the ball deflected over the top and found him in the clear, but Casper Ankergren stood up and pushed the shot wide.
Always sad to lose, no disgrace to lose to Spurs, good side, now we can all calm down and concentrate on the pre-season target of getting out of this division dunkarleeds The Dane then made an even better save when a fizzing Gareth Bale cross ricocheted off a defender and wrong-footed him, but somehow he tipped it away.
Defoe was incensed when, clean through again, he fell under the challenge of Lubomir Michalik but finally he got himself on the scoresheet, and on a night of sweet strikes on goal it came with a mis-hit.
The diminutive forward pulled back away from goal to collect Bentley's cross and though his left-footed shot was skewed it sailed into the top corner.
But with Tottenham again unable to convert their chances Leeds responded valiantly and Michalik's glancing header was smartly kept out by Spurs keeper Heurelho Gomes.
The League One side were back on level terms as Jonathan Howson hooked the ball back into the six-yard box, Jermaine Beckford's volley was parried by Gomes but Becchio followed up, having moved back onside.
Tottenham started the second half in positive manner and Michael Dawson's near post header from Bentley's corner was brilliantly tipped over by Ankergren.
Bentley, playing a third match in succession for the first time in a year, was full of endeavour and after a forceful run he hit a left-footed drive, but the inspirational Ankergren was up to the task again and touched over acrobatically.
Defoe's eventful night continued when having slid in to meet Bale's cross he was correctly given offside having edged ahead of the defender, but within moments he was in the right place at the right time.
Having been well found out on the right flank by Jermaine Jenas, Bentley sent a delightful low cross into the danger area and Defoe brushed it smartly into the net.
With Bale and Bentley superb down the flanks Spurs looked certain to add a third, and Peter Crouch hit the bar with a far post header.
Unlike at White Hart Lane there was to be no late injury time drama from Leeds and it was Defoe who raced on to a ball down the middle and calmly slotted home for his third treble of the season as his side marched into the next round in some style.
Tottenham manager Harry Redknapp: "These are difficult games. I've won and lost these games when you're fancied to win.
"This is a massive football club. It's really a Premier League club and it needs to get back where it belongs.
"Now we have another tough game at Bolton. It's not an easy place to go, but we're playing very well. We've had one defeat in 13 games."
Leeds boss Simon Grayson: "We were very good again. We passed the ball around well and competed ever so well against a top team in the Premier League.
"That's all we said to the players - give a good account of yourself and do yourselves justice.
"Nobody expected us to win apart from maybe 33,000 inside the ground and the players, but we like to think we've come out of it with a lot of credit."