After a lifeless first half, Tottenham took the lead not long into the second half through a Joel Ward own goal, who should have done better than diverting it into his own goal.
But Guglielmo Vicario was impressive in goal again, making a fine stop in the first half to deny Odsonne Edouard, and it required a brilliant strike by Jordan Ayew in stoppage time to breach the Spurs defence.
Perhaps most encouraging of all for Spurs supporters, who must now be starting to believe a title challenge is genuinely possible, was the control and poise that Postecoglou’s side showed in the second half.
For all of the control and mastery of the ball that Spurs showed in the second half, there was still a chance for Palace to steal a point.
There was also encouragement to be taken from an excellent assist by new signing Brennan Johnson, who found Son with a cut-back after Spurs had sliced through the Palace defence.