Chelsea shatter Spurs' top four bid
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
Read on besoccer.com
