Chris Wood scored a 92nd-minute equaliser on his Premier League debut for Burnley to snatch a 1-1 draw and continue Tottenham's problems at Wembley.
Spurs had lost seven of their last 10 matches at Wembley prior to Sunday's game, having been beaten 2-1 by Chelsea last time out thanks to Marcos Alonso's last-gasp winner.
But Mauricio Pochettino's men looked on track for a narrow victory thanks to Dele Alli's scrambled opener before Wood's late impact from the bench.
The striker, a club-record arrival from Leeds United earlier this week, scored the equaliser in the second minute of added time by thumping home a low finish from Robbie Brady's brilliant pass.
Alli had put Spurs ahead four minutes into the second half, smashing in a loose ball after the visitors failed to clear Christian Eriksen's corner.
But after Harry Kane, who has failed to score in 13 Premier League appearances in August during his career, wasted a string of chances, Wood came up with a priceless leveller for his side, who defeated Chelsea on the opening weekend at Stamford Bridge on their last away league outing.
Set-pieces provided the only early chances as James Tarkowski and Ben Mee headed Brady corners over the crossbar in a bright start from the visitors. Kane should have done better with a Eriksen free-kick after 17 minutes, but the England forward could not get his header on target.
A series of crucial blocks maintained the first-half deadlock as Burnley frustrated Spurs, Tarkowski brilliantly deflecting another Kane shot wide to prevent a certain goal.
But the visitors' resistance ended as Spurs forced the breakthrough with the first shot on target of the match, four minutes after the restart. Mee failed to clear a right-wing corner from Eriksen and Alli reacted quickly to slam in the loose ball for his second Premier League goal of the season.
With Burnley on the ropes following the opener, Kane missed another fine chance, drilling wide of Tom Heaton's left-hand post after being found by Eriksen.
Burnley failed to muster a shot on target against West Brom and finally called Hugo Lloris into action after 70 minutes, the Spurs captain diving to his left to keep out a fierce Brady drive as the Clarets briefly threatened to equalise.
As the game opened up Heaton made two fine saves in quick succession, the goalkeeper denying his international team-mate Kane with a fine dive to his right and then reacting well to tip Eriksen's drive over the crossbar.
Lloris raced off his line to deny substitute Wood and the striker then directed a header into the goalkeeper's arms in a late flurry.
And the New Zealand international sealed his stunning impact with a dramatic leveller, scoring his first Premier League goal since August 2014, timing his run on to Brady's brilliant pass to slam in a memorable maiden strike for the club in added time.
