The Championship side battled all the way to the bitter end and were within three minutes of an unlikely appearance in a major cup final until the late double strike from Harry Redknapp's side.
The Tottenham manager made six changes from the side that started against Portsmouth in the Premiership last Sunday, and in the early stages it was Spurs that enjoyed the majority of the possession as the Clarets struggled to get a foothold in the game.
All that changed when Robbie Blake and Chris Eagles switched flanks and it was to prove something of a masterstroke as from then on it was the home side that looked by far the better team.
Burnley were given some hope when Blake curled a lovely free-kick beyond Spurs keeper Ben Alnwick after the youngster had been caught off guard when he was expecting a cross.
Turf Moor really came to life on 73 minutes when Blake twisted and turned his way past two defenders before crossing low to the far post where the ball was turned home by midfielder Chris McCann.
Tottenham substitutes Gareth Bale and Pavlyuchenko pulled efforts wide of goal and it needed a fine double save from Brian Jensen to keep Burnley in the game.
The unlikely seemed probable with just three minutes of normal time remaining when Blake's long free-kick was spilled by Alnwick and Clarets substitute Jay Rodriguez gleefully took advantage to score.
The Burnley-born youngster has made a habit of coming off the bench and scoring vital cup tie goals this season.
It was Tottenham that created the first opportunity in extra-time with Tom Huddlestone having a shot parried by Jensen while Bale also tested the Burnley goalkeeper.
But with only two minutes of extra-time remaining it all went wrong for the home side as Pavlyuchenko turned the ball past Jensen from close range to send Spurs to Wembley.
To rub further salt into the wounds of the home team, Defoe curled a left-foot shot from the edge of the box beyond Jensen to finally put an end to the fantastic efforts of Owen Coyle's brave players.