The Championship outfit actually took the lead through Martin Paterson and such was Spurs performance in that first forty five minutes, the holders of the trophy were booed off a half time.
But then came a devastating riposte in the second period.
Michael Dawson restored parity just after the break, then Jamie O'Hara gave the Premier League side the lead.
Roman Pavlyuchenko continued his record of scoring in every round with Spurs third and Burnley's misery was complete on 67 minutes when Michael Duff headed past his own keeper.
"At half-time you could not see that result coming, that was for sure, and nor could I. At half-time I had to get in to them big time and sort a few of them out really.
"(In the second half) we were a different team. We have got to play like that all the time. We can't play like we did in the first half.
"We squeezed up second half, got in contact with them and put them under pressure."