Nathan Ake's late goal gave Manchester City their first victory in six visits to Tottenham Hotspur Stadium and a place in the FA Cup fifth round.
City looked likely to have to settle a replay after missing a succession of chances before Ake scored their first goal at this stadium after five successive defeats with two minutes left as Spurs keeper Guglielmo Vicario failed to hold Kevin de Bruyne's corner under pressure from Ruben Dias.
It was a bitter blow to Spurs after a defiant rearguard action but just reward for City, who had been the better side only to miss the opportunities that had come their way before Ake bundled home from close range.
Spurs barely registered an attack threat, while City had an early Oscar Bobb strike ruled out for offside, Vicario also saving well from Bernardo Silva. De Bruyne was uncharacteristically wasteful with a golden opportunity after Pierre-Emile Hojbjerg had gifted possession to Phil Foden.
In a dramatic finale, with a replay looking certain, Ake struck to spark wild scenes of celebration among the 9,000 City fans who had made the journey to north London.