On the back of a behind-closed-doors training ground clash with Cambridge United, the Lilywhites put out two separate XIs for the midweek encounter, where Postecoglou's second-half side did most of the damage.
Brennan Johnson drew first blood for the North London giants six minutes before the break, although after Postecoglou made a full 11 changes, Hearts levelled straight away through Lawrence Shankland.
However, the hosts' equaliser would only precede a Tottenham onslaught, as Will Lankshear restored Spurs' lead before Mikey Moore and Djed Spence also contributed to the Tynecastle Park trouncing.
A late own goal from Lewis Neilson made Tottenham's margin of victory that little bit more emphatic, on an evening where a plethora of Postecoglou's players made their case for first-team breakthroughs in 2024-25.
Djed Spence may have revived Tottenham career
One man whose Tottenham career appeared dead in the water just a couple of weeks ago, Djed Spence came on for the second half of Wednesday's friendly, replacing first-choice right-back Pedro Porro and subsequently conjuring up an unexpectedly scintillating display.
Excelling in an inverted role, the former Genoa and Leeds United loanee provided the assist for Lankshear's effort just nine minutes after his introduction, storming through the centre of the field before a delicate pass for the teenager to finish off.
Spence took up a similar position for his own strike late in the second half, as RB Leipzig loanee Timo Werner advanced to the byline down the left and played a dangerous ball into the six-yard box, where Spence arrived to tap home on the stretch.
Following the collapse of his permanent move to Genoa, and the expectation that Emerson Royal will depart in the current window, Spence's terrific display could be the start of an unforeseen redemption arc at Tottenham.
Mikey Moore sends tongues wagging again
Already regarded as the jewel in the Lilywhites' crown - apparently attracting offers from Manchester City and Manchester United - 16-year-old Mikey Moore demonstrated why Spurs should pull out all the stops to keep him.
Another second-half change from Postecoglou, Moore linked up well with new signing Lucas Bergvall, cutting inside from the right flank and taking the ball in his stride well, before finding himself up against a couple of maroon shirts.
However, the 2007-born attacker comfortably shrugged off the attention of a Hearts defender before firing in a crisp finish to make it 3-1, and as Moore turns 17 on August 11, a first professional contract should be his Tottenham's birthday present to him.
Which other Tottenham players impressed in Hearts victory?
Before Postecoglou rang the changes for the second period, the attacking big boys in Johnson, Heung Min-Son, Dejan Kulusevski and James Maddison linked up in the first half, where the seldom-seen Manor Solomon also started.
Maddison and Kulusevski were the instigators of an exquisite move for Johnson's goal with a brilliant one-two; the Swede cleverly backheeled the ball to Maddison as he made a lung-busting run into the box, before the playmaker crossed for Johnson to side-foot in a volley from close range.
With Lankshear also finding the back of the net after penning a new long-term deal, Bergvall providing a nice assist and Werner also directly contributing, Wednesday's win was one full of positives for Postecoglou, who also got a glimpse of Archie Gray and Jamie Donley in the backline.
What next for Tottenham after Hearts thrashing?
Tottenham only have two full days of recovery before they go again on Saturday, travelling to Loftus Road to meet Queens Park Rangers in their next friendly, after which they will jet off for their tour of Asia.