Keane's catalogue of misses costs Spurs
Burnley ... 2 Tottenham ... 1 Steve Davis' second-half winner capped a barnstorming Burnley comeback and sent last season's finalists Tottenham crashing out.
Davis pounced with a bullet header in the 61st minute as Stan Ternent's First Division side produced a comeback to remember at freezing Turf Moor.
Burnley - who had lost their last three games and conceded 12 goals in the process - had gone behind to Gustavo Poyet's 17th-minute header.
But Robbie Blake drove home a 58th-minute equaliser to climax a sustained spell of home pressure at the start of the second half.
Second half substitute Robbie Keane smashed an injury-time volley against the crossbar as Spurs poured forward. But a Keane equaliser would have been a travesty on a night when the Irish striker missed two of the simplest chances he will ever have.
He raced clear one minute after Blake's equaliser only to squirt a weak shot wide of Marlon Beresford's goal.
And he missed an even better chance when he bore down on goal again but, attempting a lob, scooped a weak shot straight into Beresford's arms.
Somewhere amid all the action Darren Anderton appeared as a second-half substitute for his first action in a Tottenham shirt this season and Gary Doherty made a late, ineffectual appearance.
It had not looked like Anderton's influence would be needed in the opening stages when Burnley's poor recent record looked like continuing.
Graham Branch's mistake almost let in Matthew Etherington in the first minute then Gareth Taylor was forced to hack clear after Dean West gave away a dangerous free-kick.
Steffen Iversen forced a low save out of Beresford before Poyet rose highest to meet Stephen Carr's 17th-minute corner and power an unstoppable shot past the home goalkeeper.
Iversen should have put his side further ahead when he scooped an Etherington cross over the crossbar while Burnley's lack of fire in front of goal was summed up by Blake, who trickled a poor shot straight at Kasey Keller. All that was to change after half-time, however.
BURNLEY: Beresford, West, Gnohere, McGregor, Branch, Weller, Stephen Davis, Grant, Briscoe, Blake, Taylor.
TOTTENHAM: Keller, Perry, Bunjevcevic, Gardner, Carr, Poyet, Clemence, Davies, Etherington, Iversen, Ferdinand.
Referee: D Gallagher (Oxfordshire).