Spurs secured their spot in the Champions League with victory over Manchester City on Wednesday and they looked to be cruising when Gareth Bale and Luka Modric netted inside 32 minutes.
But Wade Elliott pulled one back before the break and incessant Burnley pressure in the second half paid off when first Jack Cork levelled and then Martin Paterson put the Clarets ahead. Steven Thompson put the icing on the cake with a late fourth.
Tottenham boss Harry Redknapp made only one change from the side that beat City but it was a significant one for keeper Ben Alnwick, who made his first Premier League appearance for the club in place of the injured Heurelho Gomes.
A sizeable contingent of away fans had made the trip from London and they had a goal to cheer after only three minutes as Spurs carved Burnley apart.
A long ball from Younes Kaboul down the right put Aaron Lennon away and his cross fell perfectly for Bale, who beat the men on the line with a precise finish.
It was the Welshman's third goal in six games and the perfect way to celebrate the new four-year contract he signed this week.
At the other end, Alnwick was involved for the first time in the seventh minute, comfortably saving a shot on the turn from Cork.
Burnley have the league's leakiest defence and it was nearly breached again after 15 minutes but Peter Crouch's header from Bale's corner was a foot too high.
The Clarets were simply giving Spurs too much space and they paid for it again in the 32nd minute as Modric netted the visitors' second.
This time Burnley closed down Bale but he managed to squeeze a pass through to the Croatian in acres of space 25 yards out and he ran into the box, beat Steven Caldwell and slammed a shot high inside Brian Jensen's near post.
Having offered little threat, the hosts then pulled a goal back out of nothing three minutes before the break. Steven Fletcher's flick sent Elliott clean through and, although Alnwick got a hand to the shot, he could not keep it out.
Tottenham came within an inch of restoring their two-goal advantage immediately after the restart. Jermain Defoe played in Lennon on the right and his shot beat Jensen but struck the far post.
Burnley were not lying down, though, and King produced a superb tackle to deny David Nugent in the area before Alnwick reacted well to block the follow-up from Martin Paterson.
Fletcher then tested Alnwick at his near post before going even closer moments later. Paterson swung over a terrific cross but Burnley's leading scorer could not direct his close-range volley on target at full stretch.
But Spurs did not learn their lessons and in the 54th minute the hosts were level. Another terrific right-wing cross from Paterson was too high for Nugent but perfect for on-loan Chelsea youngster Cork, who headed in his first goal for the Clarets.
Suddenly it was Tottenham being run ragged and only a second last-ditch tackle from World Cup hopeful King prevented Fletcher getting on the end of Paterson's cross when he looked certain to score.
Redknapp responded by bringing on Roman Pavlyuchenko for Defoe and Wilson Palacios in place of Tom Huddlestone but the momentum remained with the Clarets.
The comeback was complete in the 71st minute and it was no more than Burnley deserved. Fletcher did brilliantly to hold onto the ball on the left of the area and his cross provided Paterson with a simple finish at the far post.
At the other end, a free-kick from Bale again caused problems for the Burnley defence but Crouch's effort was straight at Jensen, while the keeper also held on to a deflected shot from Lennon as Tottenham sought an equaliser.
They very nearly got it moments later but the woodwork came to the hosts' rescue again as Caldwell headed Bale's corner against his own crossbar.
But it was Burnley's day and they made sure of the three points two minutes from time when Elliott's shot from 20 yards was diverted past Alnwick by substitute Thompson.
The victory meant the hosts climbed above Hull into 18th place in the final Premier League table.