Destiny Udogie was shown a second yellow card 10 minutes after the break leaving the home side hanging on for a point.
Australian Postecoglou said his first Premier League defeat was hard to analyse.
BEST STARTTottenham have enjoyed their best start to a top-flight season since 1960 with Postecoglou the first manager to go unbeaten in his first 10 Premier League games.
Chelsea were chasing shadows initially and were relieved when Son's effort was ruled out for offside.
Minutes later Chelsea's Moises Caicedo drove a low shot home through a crowd but that was ruled offside and confirmed by VAR.
Persons:
Chelsea's Nicolas Jackson, Reece James, Moises Caicedo REUTERS, Tony Obrien, Tottenham Hotspur's, Nicolas Jackson, Mauricio Pochettino, Chelsea, Dejan Kulusevski's, Son Heung, Chelsea scuppered, Cristian Romero, Cole Palmer, Micky van de, James Maddison, Udogie, Jackson, Eric Dier, Son, Robert Sanchez, Ange Postecoglou's, Postecoglou, we're, I'm, Kulusevski's, Levi Colwill, wrongfoot Sanchez, Raheem Sterling, Romero, Colwill, Moises Caicedo, Michael Oliver, Enzo Fernandez, Maddison, Van de, Pochettino, Martyn Herman, Ken Ferris
Organizations:
Soccer Football, Premier League, Tottenham Hotspur, Chelsea, Tottenham, Spurs, Manchester City, BEST, Argentina, Sterling, Thomson
Locations:
London, Britain, Chelsea's, Sterling's, Senegal