The Whites took an early lead through Rodrigo Moreno, but hearts sank around Elland Road late on as Kenny McLean equalised for the visitors.
But there was a twist in the tale, as youngster Joe Gelhardt sparked wild scenes from the home fans, as he fired home the winner in the fourth minute of added time.
Speaking after the game, Whites goalkeeper Illan Meslier, who has made more saves than any other top tier goalkeeper so far this season, said: “It's true. (I made a match-winning save late on). In one of the last balls there was a flick on from the keeper in the box and a difficult ball and finally I stayed big.
“No 22 - Pukki - shot and I saved it with my face. I don't care if it's the hands, the face, the chest, it's a save, this is what's important!”
“It was an unbelievable game. Honestly, it was crazy because we scored in the first half but after they equalised and at the end you think oh no this is not possible but at the end when Joffy (Gelhardt) scored it was just unbelievable.
“It was like a volcano eruption. It was fantastic.”
Next up, the Whites take on Wolverhampton Wanderers on Friday night, in what should be an enthralling clash at Molineux.
Take a look at the latest news and transfer stories from the Premier League, as the reaction to last weekend's action continues.
1. Torino could cool Praet interest
Torino’s hopes of signing Leicester City outcast Dennis Praet permanently look to have taken a blow, with the Foxes said to have upped their asking price to around £12.5m. The Serie A side could opt to abandon the move, with the player’s injury history also a concern. (Team Talk) | Getty Images
2. Barca could chase Lukaku
Barcelona have been linked with a shock move for Chelsea striker Romelu Lukaku, as they fear they may miss out on Borussia Dortmund’s Erling Haaland to Man City. Lukaku has fallen out of favour at Stamford Bridge, losing his starting spot to Kai Havertz. (Daily Star) | Getty Images
3. Bremer boost for Spurs
Spurs’ hopes of signing Torino’s Gleison Bremer look to have improved, with AC Milan’s Mattia Caldara said to be currently eyed as his replacement. Torino are likely to ask for a fee in the region of £21m for Bremer. (Pianeta Milan) | Getty Images
4. Reds want Celtic starlet
Liverpool are said to be closing in on a move for Celtic wonderkid Ben Doak. The Reds are likely to be able to pick the 16-year-old, who has featured twice for the senior side so far this season, for a minimal tribunal fee. (The Athletic) | Getty Images
5. Chelsea sale could happen this month
The investment firm tasked with selling Chelsea have suggested a sale could happen before the end of the month. As things stand, the Blues can’t sell any match tickets, amid the sanctions Russian owner Roman Abramovich is under. (BBC Sport) | AFP via Getty Images
6. Atleti keen on Cash
Aston Villa ace Matty Cash is said to be one of Atletico Madrid’s key transfer targets ahead of the summer. The reigning La Liga champions had success with an English right-back last season, with Kieran Trippier playing an important role in their title winning campaign. (Marca) | Getty Images