If Tottenham end up qualifying for the Champions League next season then they will probably look back on this nerve-shredding comeback victory as a crucial moment in their campaign.

Having recovered from the shock of conceding to Tahith Chong’s smart finish in the third minute thanks to an own goal from Issa Kaboré at the start of the second half, it seemed inevitable that Ange Postecoglou’s side would go on to claim all three points and remain hot on the heels of rivals Aston Villa. But despite throwing everything at Luton including a late goalmouth scramble that saw Alfie Doughty clear the ball off the line by a matter of millimetres late on, Rob Edwards’ side looked like they had earned a crucial point until Son Heung-min struck four minutes from time to break Luton hearts.

It meant the South Korean has now moved ahead of Tottenham legend Cliff Jones into fifth place in the club’s all-time goalscoring list and, having surrendered so meekly to Fulham before the international break, the home supporters and Postecoglou could breathe a sigh of relief.

“We made the game very difficult for ourselves after conceding a disappointing goal,” said the Tottenham manager. “There’s a lot of anxiety around the place because every match means so much at this stage of the season but I thought the lads handled it really well.”

For Luton, the late defeat was a bitter pill to swallow as they dropped back into the bottom three once again after Nottingham Forest’s draw against Crystal Palace.

“I feel sick right now,” said Edwards, whose side face another trip to north London against Arsenal on Wednesday night. “Tottenham are a great team but to lose so late from our attacking set-piece is difficult to take. But to be competitive with the amount of players we have missing is a great credit to our players.”

Edwards revealed that his side’s injury woes had got so bad this week that their coach Kev Foley managed to tweak his hamstring while making up the numbers in training. So it was a patched up Luton side that took to the field for their first league encounter at Tottenham since a certain Gary Lineker scored twice in a 4-1 victory at the old White Hart Lane in November 1992.

Not that it seemed to faze them. A quick break in the third minute that began when Andros Townsend robbed Son of possession and sped downfield ended with Chong finding the back of the net via Guglielmo Vicario’s far post after being picked out superbly by Ross Barkley’s clever square pass across the area. “Conference champions, you’ll never sing that,” sang the away supporters in delight.

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Tottenham enjoyed 74% of possession in the first half but squandered a number of opportunities to draw level. Dejan Kulusevski’s brilliant long ball played in Timo Werner, only for the German – preferred to Brennan Johnson in Tottenham’s solitary change from the Fulham defeat – to miss the target with the goal gaping. Only Luton will know how they survived the next attack, with Son’s shot coming back off both posts before Werner and Pape Sarr saw their goalbound efforts blocked by Kaboré and then Teden Mengi.

Postecoglou’s hands remained rooted in his pockets when Werner gave away possession to stall a promising attack, whereas Edwards was a whirl of arms on the touchline as he cajoled his team into position. Watched on by David Pleat, the former manager whose name is synonymous with both these clubs, it seemed to be working as Luton effectively shut down the game. Postecoglou headed down the tunnel to a small number of boos from the home fans.

It was perhaps surprising to see Kulusevski rather than the ineffective Werner replaced by Johnson at the break, while Luton were forced into a defensive change as Daiki Hashioka came on for the injured Reece Burke. The former Forest player had an instant impact when a one-two with Pedro Porro allowed him to whip in a dangerous cross that was turned into his own net by Kaboré under close attention from Werner.

Somehow Luton were hanging on after another last-ditch clearance from the outstanding Kaboré. Porro fired over from close range before Son somehow failed to convert from two yards out thanks to a combination of Thomas Kaminski and a desperate last-ditch clearance from Doughty. But it was Son who had the final say when he fired home after being set up by Johnson and allowed Postecoglou to finally celebrate.

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