With less than three minutes of extra-time left at Turf Moor, the second-tier side were on course to go through to a 1 March meeting at Wembley with world champions United on the away goals rule. At that stage the tie was all square at 4-4 on aggregate, with the Clarets 3-0 ahead in the second leg courtesy of goals from Robbie Blake, Chris McCann and Jay Rodriguez.
However, Pavlyuchenko edged Spurs in front overall before Defoe's 120th-minute effort made sure Tottenham manager Harry Redknapp, who won the FA Cup with Portsmouth last season, would be heading back to Wembley after a dramatic 6-4 aggregate success.
Burnley, who had already knocked Premier League sides Fulham, Chelsea and Arsenal out of the League Cup this season, were 100-1 rank outsiders to go through before the second leg kicked off. But on a windswept and rain-drenched evening in the north-west, Burnley, on the fringes of the race for promotion to the Premier League, made a mockery of those odds.
Ben Alnwick made his Spurs debut as first-choice goalkeeper with Heurelho Gomes missing for the top-flight strugglers through injury, along with Ledley King, Vedran Corluka and Aaron Lennon. Meanwhile Pavlyuchenko, who has now scored in every round of the competition, was dropped to the bench along with Gareth Bale. The Clarets were themselves weakened through the absence of suspended captain Steven Caldwell and cup-tied striker Steve Thompson, with Wade Elliott and Blake filling in respectively.
Tottenham almost scored first when Jonathan Woodgate - one of just two survivors, along with Didier Zakora, from the Spurs side that beat Chelsea 2-1 in last year's final - headed over from David Bentley's corner. But instead it was Burnley who broke the second-leg deadlock. They were awarded a free-kick for Woodgate's foul on Joey Gudjohnsen and from fully 25 yards out, Blake beat Alnwick at the keeper's near post with a superb curling effort.
Clarets manager Owen Coyle had said beforehand his side would need "to scale Everest and beyond" to reach the final, but now the summit was in sight. Midway through the second half, Tottenham had the chance to draw level in the second leg when Defoe pounced on an error by Clarke Carlisle but Burnley goalkeeper Brian Jensen moved smartly off his line to deny the England striker.
Burnley continued to press forward and in the 73rd minute a cross from Blake was turned in at the far post by McCann. Spurs' advantage was erased with two minutes of normal time left when, after Alnwick fumbled Blake's free-kick, substitute Rodriguez scored. At the end of normal time, Martin Paterson's first-leg goal for Burnley, which had seemed as if it would be a mere footnote, meant the Clarets were still in the tie.
Now, however, they had a position to defend and the character of the match changed with Spurs making the running in the first half of extra-time. But Burnley did not concede and were in sight of a first League Cup final appearance when Pavlyuchenko, who came on for Luka Modric midway through the second half, scored from six yards in the 118th minute. And moments later Defoe grabbed another goal to make sure of an all top-flight encounter with United, 4-3 aggregate winners over Derby County yesterday.