As well as seeking an instant response to their 3-0 humiliation at the hands of Fulham before the international break, Tottenham knew that victory over the Hatters would temporarily propel them back into the top four of the table over Aston Villa on goal difference.
However, in what has become a frequent occurrence in Premier League home games, Tottenham fell behind first, as Tahith Chong made the most of pitiful Spurs defending to break the deadlock in the third minute.
For all of their attacking endeavours, Tottenham lacked a ruthless edge in the first 45 minutes, but the half-time introduction of Brennan Johnson breathed new life into the North London giants, as Issa Kabore diverted the Welshman's cross into his own net.
The former Nottingham Forest man's heroic cameo concluded with the assist for Spurs' winner in the 86th minute, as he teed up Son Heung-min to fire a deflected strike past a diving Thomas Kaminski, thus completing another second-half turnaround for the hosts.
Johnson bounces back from Wales heartbreak
Johnson's game-changing display came after the attacker suffered Euro 2024 qualifying heartache with Wales, who lost to Poland on penalties in their playoff final, and Postecoglou was asked about the attacker's mental state in his post-game press conference.
"I know you want me to give them all a cuddle, mate. I know you are always concerned about our players, but I just don't have the time. I don't have the time," football.london quotes the Australian as saying.
"There are 25 beautiful souls in my dressing room and I just don't have the time to get around to them. It's football you know. It's a hard business, there's ups, there's downs and you've just got to deal with them sometimes.
"Brennan, obviously like Benny, felt the pain of missing out on a major competition, but being a professional footballer you use that as motivation to go out there next time. I am sure Brennan has got another couple tournaments in him and next time he'll try to become the one that gets them there."
Tottenham's first-half woes continue
Before Johnson's introduction turned the game on its head, Tottenham fans witnessed another sluggish start from their beloved side, who have now failed to score in the first half of each of their last six Premier League.
The Lilywhites have to go even further back to December's win over Bournemouth for the last time that they scored in the first half of any home match - enduring a streak of seven without an early goal at the Tottenham Hotspur Stadium since the turn of the year.
However, Postecoglou is not stressing too much about his side's lack of first-half goals and instead took the most issue with the manner in which his side conceded on Saturday, adding: "I don't know, no, not really. The disappointing thing about the first half is the goal we conceded.
"Our football was good. We created good chances, one-vs-ones, we hit the post, they blocked quite a few shots and they defended desperately. I think overall there was nothing wrong with our football. The goal we conceded, yeah that was poor and that's something we need to address.
"With a lot of our football it becomes a war of attrition. We need to put pressure on the opposition because we know we're going to run our games really strongly and I thought we made Luton work really hard in the first half and I thought you saw in the last 10 to 15 minutes that they paid the price for that."
Tottenham spent just a couple of hours in the top four before being bumped back down to fifth thanks to Villa's win over Wolverhampton Wanderers, and next up for the Lilywhites is a London derby away to West Ham United on Shrove Tuesday.