The clock had ticked into the 86th minute when Heung-min Son collected the ball deep in his own half and summoned the energy for another forward run.
Tottenham had hammered away at Luton for most of the second half, having gone behind early in the game and then equalised soon after half time.
Son released Timo Werner and kept on running. Werner found a change of pace and crossed the ball low from the left. Brennan Johnson poked it back and the Spurs captain arrived to find the net with the help of a deflection.