After looking lacklustre for much of the game, Tottenham’s surge forward in search of an equaliser came all too late.
Son Heung-min was agonisingly close to netting an 89th-minute leveller as he slided in to reach Brennan Johnson’s cross, but Robert Sanchez scrambled across his goalline brilliantly to deny the Spurs captain.
While Chelsea constantly hassled their visitors, Tottenham looked panicked in defence, sloppy in possession and struggled to fashion many clear-cut chances.
Vicario, meanwhile, provided little reassurance to his backline with multiple wayward passes and an inability to command his box convincingly.
Frustrations boiled over on the stroke of half-time when Cristian Romero’s shove on Levi Colwill caused a maul as players squared up to each other.
But Tottenham were unable to channel their emotions into anything worthwhile.
And in the wake of this defeat, Postecoglou’s future at the club becomes all the more uncertain.
Some away fans directed chants of “you don’t know what you’re doing” at the Australian manager, who becomes the first-ever Spurs boss to lose his first four fixtures against Chelsea.
But there is still a hope for success in the Europa League – and a first trophy since 2008 – with a quarter-final first leg against Eintracht Frankfurt next week.