Pavlyuchenko rifled home with two minutes of extra-time remaining
Roman Pavlyuchenko and Jermain Defoe scored late in extra-time to break Burnley's hearts and send Tottenham through to the Carling Cup final.
Burnley had been two minutes away from reaching Wembley as they led on the away goals rule with them 3-0 up on the night and the aggregate score at 4-4.
Robbie Blake put the Clarets ahead on the night and Chris McCann made it 2-0.
Jay Rodriguez forced extra-time with a volley, but strikes from Pavlyuchenko and Defoe won it for Spurs.
It was a devastating blow for Burnley, who had looked set to complete a sensational comeback against opponents who were rated at 1-100 to reach the final before the incredible events unfolded at Turf Moor.
Spurs will be hugely relieved, and are highly fortunate to go through after they produced a lethargic approach and some awful finishing that very nearly cost them.
Burnley had given warning that they would be no pushovers after a decent first-leg display at White Hart Lane that belied the scoreline.
And they must be given tremendous credit for their spirit, belief and desire which almost brought them a result that would have given Tottenham nightmares not suffered since 2004 when they lost 4-3 to Manchester City in the FA Cup, despite leading 3-0 at half-time and playing against 10 men.
Burnley's best chance of achieving what many people believed to be impossible was always to score early on and put Spurs under pressure.
And they were almost gifted that dream scenario when Benoit Assou-Ekotto chipped the ball back to his keeper from 30 yards out and Ben Alnwick had to scramble backwards to claw the ball wide as it threatened to sail over his head.
It seemed to set a pattern for Spurs, who proceeded to play with a lack of care.
Aside from a skidding Defoe shot, that was pushed wide by Brian Jensen, the visitors struggled to get out of their own half.
Dominating both territory and possession, Burnley must have sensed that they could at very least give the aggregate scoreline some respectability.
But it was easy to see why Burnley had won only once in their last six matches as they struggled to create any clear-cut openings.
McCann shot wide from 20 yards, while Wade Elliot tamely chipped off target from inside the box.
But then Burnley got the breakthrough their all-round play had deserved.
When Blake lined up a free-kick, he was offered a significant portion of the goal to aim at as Alnwick took up a woeful position, and the forward duly curled the ball into the space.
Just as the hosts looked to build, they lost Stephen Jordan to injury and had to replace him with Christian Kalvanes.
While the reshuffle did affect them, it was more a case of the conditions preventing Burnley dominating the match after the break.
With the strong wind against them - and Tottenham in less lethargic mood - the game had a more even feel to it.
And had Luka Modric kept his shot down, after a superb turn had earned him space, Spurs would have completely killed off Burnley's hopes of a comeback.
The Londoners got an even better chance to seal their passage to the next round when substitute Gareth Bale, on for the injured Jamie O'Hara, was clean through but he screwed his shot hopelessly wide.
Rodriguez kept his cool with his volley to send the tie into extra-time
Instead it had the effect of stirring the hosts into redoubling their efforts and the inspirational Blake squared to Paterson, but he blazed over.
Blake, though, was rewarded later for some superb work on the wing, where he beat two players before squaring the ball for McCann to slot in from six yards.
Now the comeback was well and truly on and Burnley piled forward in search of a third goal, which would send them through to the final on the away goals rule in extra-time.
However, it meant there was space at the back for Tottenham to exploit and they should have wrapped up the tie when Bale played in substitute Pavlyuchenko but he spooned the ball wide from close-range.
It was a miss that was to prove costly as Burnley made it 3-0 and forced extra-time when Rodriguez slammed in after Alnwick had dropped Blake's free-kick.
Yet there was to be another twist in the tale of a match that will be talked about for decades.
As the Burnley players' legs tired, Assou-Ekotto pulled the ball back to Pavlyuchenko, who smashed the ball in to put Spurs ahead on aggregate - and keep up his record of scoring in every round of the competition.
Burnley's misery was compounded when Defoe beat his marker and bent in a shot from the edge of the penalty area to seal Tottenham's date with Manchester United at Wembley.
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