The Clarets were behind after just 68 seconds - the quickest goal they have conceded in the Premier League - when Gareth Bale turned home Heung-Min Son's cross.
Harry Kane made it 2-0 after a quarter-of-an-hour when his effort, from Bale's pinpoint pass, took a deflection off James Tarkowski.
Lucas Moura then made it 3-0 before the break when Burnley failed to deal with Sergio Reguilon's delivery.
Bale then grabbed his second of the afternoon with a sumptuous left-footed finish in the 55th minute.
Here are the RATINGS from the Tottenham Hotspur Stadium.
1. Nick Pope 4.4
Spent most of his afternoon picking the ball out of the net, but could hardly be blamed for any of the home side's goals. Made a couple of superb second half saves to deny Kane and Son.
2. Matt Lowton 4.1
One of Burnley's better performers. Used the ball better than most, swinging the ball in behind the Spurs defence in open play, and tried to cut out Reguilon's threat at the earliest point possible.
3. Charlie Taylor 3.8
Faced with a whole manner of different threats down his side. Played Bale on for the opener, the quickest Burnley have conceded in the PL, and couldn't get close enough to the Welshman when Spurs broke for his second of the afternoon.
4. James Tarkowski 3.6
Overpowered by Kane and pulled here, there and everywhere by Spurs' interchanging front four. Had a helping hand in the home side's second, culpable for the third and caught too high up the pitch for the fourth.