Nuno Espirito Santo's side blew a two-goal lead and then wasted a 3-2 advantage, but still finished with all three points in one of the Premier League's most exciting games of the season at Molineux.
Jota was Wolves' hero with his winner deep into stoppage-time, capping a dramatic finale that left Puel holding his head in disbelief at the final whistle.
This was a third successive defeat for Leicester, including an embarrassing FA Cup exit at minnows Newport, leaving Puel facing a fight to hold onto his job.
The Frenchman had already endured numerous reports that he was on borrowed time at the King Power Stadium amid reports of player and fan unrest.
Wolves were quickly into their stride and took the lead in the fourth minute when Joao Moutinho's cross picked out Jota and the Portugese midfielder guided a close-range volley past Leicester keeper Kasper Schmeichel.
Jamie Vardy almost snatched an equaliser when Wolves goalkeeper Rui Patricio got his feet in a tangle, gifting possession to the Leicester forward before scrambling back to save at the last moment.
Ryan Bennett doubled Wolves' lead in the 12th minute, the defender rising above Harry Maguire to met Moutinho's corner with a bullet header for his first goal of the season.
Leicester pulled a goal back two minutes after the break as Vardy found Demarai Gray, who skipped past a challenge and fired home with a blistering strike.
Harvey Barnes, on his first Premier League start for Leicester, played the crucial role in the 52nd minute equaliser when the young midfielder's shot deflected in off Wolves defender Conor Coady for an own goal.
Wolves regained the lead in the 64th minute when Ruben Neves's pass sent Jota clear on goal and he chested down before drilling a shot that Schmeichel could only push into the net.
In the 87th minute, Wes Morgan charged onto James Maddison's free-kick and climbed above three Wolves defenders to thump a close-range header past Patricio.
But Jota had the last word in the third minute of stoppage-time as he raced onto Raul Jimenez's pass and slotted home with the Leicester defence completely out of position.
Jota's winner sparked wild celebrations from Santo, who ran onto the pitch to join his jubilant players, earning a dismissal in the process.AFP