In a thrilling race on Sunday, Hamilton – who is on 99 career victories – had to charge up through the field just to claim a podium finish at a track where he has won on eight previous occasions.
Hamilton started in pole position, yet a crash at Turn One caused by his team-mate Valtteri Bottas, who has been handed a five-place grid penalty for the next event in the season, resulted in the need for the red flag.
Max Verstappen, Hamilton's championship rival, was involved, though the Red Bull driver managed to continue – albeit in a heavily patched up car.
Five other drivers, including Bottas, were not so fortunate, but upon the restart, Mercedes made an error when they advised Hamilton more rain was scheduled to arrive at the Hungaroring.
However, the skies had cleared and the track had already dried up. With every other remaining driver electing to switch to dry tyres, Hamilton was left as the only car on the starting grid.
Mercedes realised the situation quickly but, by the time Hamilton had pitted, he was stuck last in 14th place, forcing him to battle his way back to secure a quite remarkable third place, behind maiden F1 race winner Esteban Ocon and veteran campaigner Sebastian Vettel.
"Today was definitely tough, we always make it difficult for ourselves," said Hamilton, who looked visibly exhausted on the podium.
"It's crazy to think we were the only ones on the grid at the start, but these things happen and we learn from them. I gave it everything, and I had nothing left at the end.
"I was telling the team how the track was through the formation lap, but they said rain was coming when I got back in the car, so I thought they had other information. I then saw everyone diving in [to the pits].
"We came in this weekend and didn't know how it was going to go and considering the circumstances today, I'll take it."
Hamilton and Mercedes at least had a better race than Red Bull. Sergio Perez was one of the drivers to crash out, along with Bottas, Charles Leclerc, Lance Stroll and Lando Norris, while Verstappen just scraped into the points in 10th.
It means Hamilton now holds a six-point lead over Verstappen at the top of the drivers' standings, while Mercedes also top the constructors' championship heading into an extended mid-season break, with the next race – in Belgium – scheduled for August 29.
"Again, taken out by a Mercedes, it's not what you want. From then on, I was missing the whole side of my car, the floor was damaged as well, it was almost impossible to drive to be honest. I still tried my best and I scored one point, it is at least something, but of course not what you want," Verstappen told Sky Sports.
"No, it's not [a reset]. These moments, they're just disappointing but I know that when we go again after the break I will be there again. I hope my car is going to be competitive, we'll find out.
"It's a lot of freak moments at the moment that have cost us a lot of points. We will never give up, we have to focus on ourselves, we'll keep pushing and see where we end up."
Ocon, meanwhile, was overjoyed to seal his first ever F1 race triumph. The 24-year-old Frenchman secured Alpine's maiden victory under its new name, and its first as a team since Kimi Raikkonen won the 2013 Australian Grand Prix.
"What a moment," Ocon said. "We've had some difficult moments this season, but we are back where we belong.
"Sebastian put me under big pressure but we managed to keep him off, so it's a great moment."