Chelsea delivered a hammer blow to Tottenham's hopes of qualifying for the Champions League with a 2-0 win against their spluttering London rivals on Thursday.
Trevoh Chalobah's first goal since March 2022 put Chelsea ahead in the first half at Stamford Bridge.
The much-maligned Nicolas Jackson wrapped up the points in the closing stages with his 14th goal of a difficult first season with the Blues.
After losses to Arsenal and Newcastle, fifth-placed Tottenham's third successive defeat leaves them seven points behind fourth-placed Aston Villa.
Tottenham have four games left, while Villa have three to go, making the north Londoners rank outsiders to finish in the Premier League's top four.
It was another painful setback for Tottenham, who have squandered the good will built by Postecoglou for much of the Australian's first season in charge.
While Postecoglou licks his wounds, Chelsea boss Mauricio Pochettino enjoyed a second win over his former club this season following the 4-1 success in November.
Pochettino had irritated Chelsea fans by admitting he couldn't "hide his emotions" for the club he managed for five years and led to the 2019 Champions League final.
But he put those feelings aside to provide the result they wanted, keeping alive eighth-placed Chelsea's hopes of qualifying for Europe and making it just one defeat in 34 home league games against Tottenham.
Postecoglou had criticised Tottenham's sloppy performance in Sunday's 3-2 defeat against Arsenal and responded by making five changes, with Richarlison brought in and James Maddison dropped.
But in Pochettino's 400th match in English football, the Chelsea manager should have been celebrating a goal inside five minutes.
Reeling Spurs
Jackson sprinted into the Tottenham area for a shot that went under Guglielmo Vicario but lacked the power to beat Mickey van de Ven's clearance off the line, with Cole Palmer somehow scooping the loose ball over from close-range.
Moments later, Chelsea winger Noni Madueke embarked on a dynamic run before firing just over from the edge of the area.
Four of the five goals conceded by Tottenham in their previous two games had come from set-pieces and they were punished for more woeful dead-ball marking in the 24th minute.
Conor Gallagher's free-kick looped into the area and Chalobah was left unmarked to power a superb header over Vicario from 12 yards.
That made it 22 goals conceded from set plays in league games by Postecoglou's creaky defence this term.
Tottenham claimed Chelsea defender Marc Cucurella had blocked Brennan Johnson from marking Chalobah, but VAR ignored their protests.
Mykhailo Mudryk's deflected strike was held by Vicario before the Ukraine winger curled narrowly wide as Chelsea pushed for a second goal.
Undone by their set-piece frailties, Tottenham almost took advantage of Chelsea's defensive deficiencies with a Cristian Romero header that clipped the post from Pedro Porro's free-kick.
Postecoglou looked increasingly irate by the half-time whistle and his chastened players responded to their manager's frustration with a more lively second half display.
Porro's drive from a tight angle forced Djordje Petrovic to save in Tottenham's most threatening moment.
But Chelsea landed the knockout punch in the 72nd minute.
Palmer's fierce free-kick cannoned down off the bar towards Jackson, who reacted quickest to head home from six yards.
