Burnley boss Sean Dyche re-wrote the script but his ‘Famous Five’ were cruelly denied a happy ending as Tottenham struck with an injury-time winner.
Dyche moved away from the regular back four to play five at the back in a bid to stifle the title challengers and build on a first win in nine games.
And for 90 minutes the plan worked to near perfection as the Clarets defended superbly – with a back line bolstered by the addition of Kevin Long ably supported by the four midfield men in front of them and an inspired Joe Hart at their backs.
But as is so often the case against the big guns, just when a morale-boosting point and a second successive clean sheet was within touching distance it was snatched away as Spurs substitute Christian Eriksen pounced at the death.
The relief around Wembley among the home supporters and the Tottenham bench was palpable.
Burnley, on the other hand, were left crestfallen as their monumental effort counted for nothing – bar the knowledge that they have another string to their bow for the battles ahead.
The switch in formation certainly worked as the Clarets kept Tottenham at arm’s length and stopped them picking holes in Burnley’s back line in the opening stages.
There was also an occasional threat on the break from the visitors with added freedom for the wide players as both Robbie Brady and former Tottenham man Aaron Lennon forced corners in a spell of Burnley pressure.
But Tottenham weren’t without chances as they looked to spring a man in behind the Clarets’ rearguard, Lucas Moura poking a lovely effort inches wide first time from Eric Lamela’s lofted pass.
Spurs also had a decent shout for a penalty when Tarkowski clipped England colleague Harry Kane in the box.
And with half an hour gone it took a fine save from Joe Hart to keep the Clarets level.
The chance came from a move started in Tottenham’s own penalty area with a free-kick awarded against Robbie Brady for dangerous play as he lifted his boot to head height.
The Clarets had been denied a penalty against Brighton the week before for a similar incident – not lost on Dyche – but this time a foul was given and Spurs countered with Moussa Sissoko finally feeding Lamela for a shot Hart blocked as he raced off his line.
Hugo Lloris had not been extended at the other end, but a minute before the break the Tottenham captain cleared sloppily to Phil Bardsley, whose cross was met by a header from Ashley Barnes which he put over the top from the Clarets’ best chance of the half.
Spurs had made five changes to their starting line-up as they juggled their resources between a Champions League tie in Barcelona and next Wednesday’s League Cup quarter-final with North London rivals Arsenal.
With the top four of the Premier League so tight their need for points remained just as acute, however, and three minutes into the second half they faced the threat of losing ground as the Clarets almost grabbed the lead.
Again Barnes – who twice scored against Tottenham at White Hart Lane – posed the threat as he met Lennon’s pull-back from a Robbie Brady free-kick with a thumping volley blocked in front of goal by Toby Alderweireld.
Barnes performed a Herculean task in trying to offer the Clarets as an outlet but increasingly the game was played in Burnley’s half as Tottenham cranked up the pressure in search of a winner.
Eriksen and Heung-Min Son were both sent on by Mauricio Pochettino and Hart made another outstanding save to deny Lamela again from close range.
With the Clarets defending heroically in front of the England man – no stranger to Wembley – Tottenham’s frustrations grew.
The introduction of Fernando Llorente was their last roll of the die and the big targetman laid on a chance for Son he screwed badly wide.
Alli then stabbed an effort into the side netting from a Son cross in the 90th-minute but in stoppage time the Clarets finally cracked as their brave resistance was ended.
Tottenham’s weight of numbers in attack proved just too much as Llorente flicked on a long ball, Kane laid it off for Eriksen and his finish gave Hart no chance to leave Burnley beaten but unbowed.
Tottenham: Lloris; Trippier, Davies, Alderweireld, Rose; Sissoko, Skipp (Son 75); Lamela (Lorente 82), Alli, Moura (Eriksen 64); Kane. Substitutes: Gazzaniga, Winks, Walker-Peters, Eyoma.
Burnley: Hart; Bardsley, Long, Tarkowski, Mee, Taylor; Lennon (Vokes 90), Cork, Westwood, Brady (Hendrick 90); Barnes (Wood 80). Substitutes: Heaton, Lowton, Gibson, Vydra.
Booked: Brady, Bardsley
Referee: Graham Scott