The First Division outfit were irresistible in the opening 20 minutes after the break after we appeared in control of the tie at half-time.
Gus Poyet opened his season's account with a bullet header from Steve Carr's corner after 16 minutes and there were further chances as well as the home side struggled with our slick passing and movement - Stan Ternent was even forced into an early tactical substitution.
Steffen Iversen twice, Matty Etherington, Poyet again and Les Ferdinand all had chances as well as Clarets were reduced to two efforts at goal.
But whatever they put in the tea at half-time at Turf Moor should be marketed. Ternent's men were unrecognisable and, in that 20-minute spell, pushed us further than any other side this season.
With Robbie Blake pulling the strings, Gareth Taylor twice and Blake himself went close before the leveller on 58 minutes as Blake's shot from the edge of the box deflected off Gardner beyond Kasey Keller.
Within a minute Robbie Keane, on at half-time, had the first of three one-on-one chances, clipping the ball over Beresford but a yard wide.
It took Burnley a further three minutes to go ahead. It was a carbon copy of our goal as Blake swung in the corner met powerfully by Steve Davis from 10 yards.
Blake then hit the inside of the post after intercepting Clemence's pass. That would have killed the game off but in the end it was Burnley hanging on.
Keane went through again after 78 minutes, his attempted chip falling short and again two minutes from time, this time Beresford was out smartly to block with his legs.
When all seemed done and dusted, Keane almost atoned for the misses in spectacular fashion, thundering a volley onto the crossbar in injury time.
That might have been harsh on Burnley, but on the night, it wasn't to be.
MINUTE-BY-MINUTE GUIDE TO THE ACTION
4mins: Wicked Etherington cross met by Iversen, powerful header almost carried over line by Beresford as he made save.
6mins: Davies cross, awkward height, volleyed over by Ferdinand.
13mins: YELLOW. Carr for foul on Briscoe.
16mins: GOAL. Carr corner met by bullet header by Poyet, 10 yards out, right corner of goal, no chance for Beresford. 1-0.
19mins: CHANCE. Quick feet from Etherington down the left, cross slightly deflected, Iversen, 15 yards out on his left foot, volleyed over.
24mins: YELLOW. Briscoe for foul on Carr.
26mins: Lovely vision from Poyet released Etherington down the left, looked to chip keeper, ball just brushed top of the net.
26mins: SUB. Little for McGregor.
27mins: CHANCE. Blake perfect pass found Taylor behind Gardner, always stretching, could only volley across goal from close range.
34mins: Bit of trickery from Carr into the box, laid ball back for Davies, cross met by Poyet straight at Beresford.
35mins: Briscoe shot deflected but Keller always in control.
40mins: Burnley's best move, West cross played back to Blake by Taylor but sliced shot wide.
42mins: Move from one end to the other started by Carr in right-back slot through Perry, Bunjevcevic to overlapping Etherington, he slid in pass to Ferdinand in the box but Beresford out quickly to block effort.
43mins: CHANCE. Carr cross flicked on by Ferdinand, Iversen didn't get hold of close-range volley.
44mins: YELLOW. West for foul on Etherington.
Half-time: Burnley 0-1 Spurs
Half-time: SUB: Keane for Ferdinand.
47mins: Deep cross from from Blake met by Taylor at the far post but header always rising too high.
51mins: CHANCE. Cross by Branch knocked back into danger area by Blake, Taylor's volley blocked by Bunjevcevic, West smashed rebound into stand.
52mins: Blake shot just over.
55mins: Poyet flashed 30-yard shot straight at Beresford.
58mins: GOAL. Blake shot from edge of the box appeared deflected off Gardner, Keller no chance. 1-1.
59mins: CHANCE. Keane through one-on-one, clipped ball over Beresford but a yard wide.
60mins: SUB. Anderton for Etherington.
62mins: GOAL. Carbon copy of our goal - corner by Blake headed home by Davis. 1-2.
64mins: WOODWORK. Clemence's pass intercepted by Blake who carried ball forward, beat Clemence and shot against the inside of the post.
73mins: YELLOW: Bunjevcevic for foul on Little.
78mins: CHANCE. Iversen header found Keane wrong side of Davis, tried to lift the ball over Beresford but ended up only chipping it into his hands.
82mins: SUB. Doherty for Iversen.
85mins: SUB. Popadopoulos for Blake.
86mins: CHANCE. Little away from Bunjevcevic into box, superb save by Keller to deny from 10 yards.
89mins: CHANCE. Keane through again, did well to hold off Davis, low shot saved by Beresford's legs.
Injury time: WOODWORK. Thunderous volley from Keane, 25 yards out, rattled the crossbar.
Line-ups: Burnley: Beresford, West, Davis, Weller, Briscoe, Gnohere, Taylor, McGregor (Little, 26), Branch, Blake (Papadopoulos, 85), Grant. Subs: Cook, I Moore, A Moore.
Spurs: Keller, Carr, Bunjevcevic, Gardner, Perry, Davies, Poyet, Clemence, Etherington (Anderton, 60), Iversen, Ferdinand (Keane, 45). Subs: Hirschfeld, Doherty, Acimovic.
Burnley's blistering start to the second half cut short our hopes of matching, if not going one better, last season's run to the final of the Worthington Cup.