Tottenham manager Harry Redknapp had perhaps surprisingly named a near full-strength starting 11 although he was without goalkeeper Heurelho Gomes - Ben Alnwick deputising for the Brazilian.
The visitors raced to an early lead when Younes Kaboul supplied a pass inside Danny Fox to Spurs wideman Aaron Lennon whose cross was turned in by Gareth Bale.
Striker Peter Crouch had two opportunities to increase the lead further before Tottenham did score their second when midfielder Luka Modric's shot left Burnley goalkeeper Brian Jensen with no chance.
The Clarets grabbed a lifeline prior to the half-time interval with a move involving Graham Alexander and Steven Fletcher before Wade Elliott's shot found the back of the net.
Spurs went desperately close to restoring their two-goal advantage early in the second half when Jermain Defoe's pass found Lennon whose shot struck the far post.
The home side then found some urgency in their play and, after Fletcher had twice gone close, grabbed a deserved equaliser when Martin Paterson's cross from the right was headed in by on-loan Chelsea midfielder Jack Cork.
Burnley continued to take the game to their opponents and were rewarded in fortunate circumstances when Fletcher mis-hit his shot across the face of goal and the ball was turned in at the far post by Paterson.
To complete a remarkable turnaround, substitute Steven Thompson grabbed a fourth by turning the ball past Alnwick after a strike from Elliott on the edge of the box.
The victory leaves Burnley chairman Barry Kilby with a tough decision to make about whether manager Brian Laws is the man who will be entrusted to see if the Clarets can spring an immediate return to the Premiership.