A Robbie Keane brace helped Martin Jol win his first game as Spurs manager.
Keane, the beneficiary of exceptional passes from Michael Carrick and Jermain Defoe, scored with two close-range finishes on 32 and 52 minutes.
Soon after, the Republic of Ireland striker turned provider, flicking the ball into the path of Defoe, who curled an exquisite shot past Brian Jensen.
Burnley had plenty of chances, notably in the first-half, but they were never able to match the Spurs' sharpness.
Robbie Blake was at the centre of the best of their attacking play, but Burnley were denied by a mixture of uncertain finishing and Paul Robinson's fine goalkeeping.
Blake signalled his threat early on, spinning swiftly away from Nourredine Naybet only to send his shot the wrong side of the post.
A good interchange of passes involving Amadou Sanokho then allowed Blake to break into the box and from his cross Richard Duffy should have done better with his header.
Having survived those early scares Spurs began to take control of midfield, with Carrick, making his first full start, linking the play impressively.
After Noe Pamarot had gone close with a couple of headers, Carrick surged down the right before checking inside.
Carrick looked up and delivered a precise pass behind the Burnley defence, which Keane collected before sweeping the ball past Jensen.
Soon after Keane delivered an equally perceptive pass to release Stephen Kelly, who was thwarted by Jensen quickly rushing out from his goal.
To their credit Burnley finished the half strongly, Tony Grant and Mike Duff forcing reaction saves from Robinson, while Blake once more stole away from Naybet only to screw his shot wide.
Keane's second goal soon after the restart completely stifled any hope Burnley might have had of causing an upset.
In tandem with Reto Ziegler, Defoe opened up the Burnley defence down the left, before the England international curled the ball with the outside of his boot into Keane's path.
Whereas for his first goal Keane had had to get the ball past Jensen, this time Defoe's pass was so good that all the Irishman had to do was touch the ball into an empty net.
Six minutes later Keane's sublime touch sent Defoe scampering away and the England international provided the perfect finish, curling the ball into Jensen's top right-hand corner.
Keane was then withdrawn by Jol with Frederic Kanoute coming on.
Kanoute's strong running exposed the Burnley defence on a couple of occasions, but Spurs were unable to add to their lead.
Burnley: Jensen, Roche, Camara, Duff, Cahill, Duffy, Sanokho,
Hyde, Grant, Branch (Valois 41), Blake, Valois (Pilkington 82).
Subs Not Used: O'Neill, Scott, Yates.
Tottenham: Robinson, Kelly, King, Naybet, Pamarot (Ifil 77),
Ziegler, Carrick, Brown, Pedro Mendes (Davies 62),
Keane (Kanoute 64), Defoe.
Subs Not Used: Keller, Redknapp.
Goals: Keane 31, 52, Defoe 58.
Ref: G Poll (Hertfordshire).