The seven-time world champion, winner a record eight times in Hungary, lapped the Hungaroring with a fastest time of one minute and 17.811 seconds.
Red Bull's runaway championship leader Max Verstappen was second fastest, 0.250 slower, with Mexican teammate Sergio Perez third and Nico Hulkenberg a surprise fourth for Haas and all on soft tyres.
Verstappen, who complained about a lack of grip, is 99 points clear of Perez and chasing his ninth win in 11 races and seventh in a row. Red Bull are hoping for a record 12th successive victory and have brought an upgraded car.
McLaren's Lando Norris was fifth, 0.271 off the pace, but the sole driver in the top 10 setting his best time on the medium tyres.
Mercedes' George Russell was sixth fastest with the Ferraris of Charles Leclerc and Carlos Sainz behind him in seventh and eighth with some drivers struggling in the gusting winds.
Hamilton had been only 16th in Friday's second practice, the only meaningful session of the day after rain in the first, with Russell last.
He has an incredible record in Hungary, however, taking his first win with Mercedes there a decade ago after wins with McLaren in 2007, 2009 and 2012. He has also been on pole a record eight times.
"This tyre format is weird because nobody really understands where you are," said Mercedes team boss Toto Wolff of an "Alternative Tyre Allocation" being trialled in Hungary with fewer sets available.
"We were only able to run one medium yesterday and that wasn't good at all. And then we put the soft on for the first time this weekend and the grip was very good.
"And then obviously Lewis here... he's just able to add another two or three-tenths," the Austrian told Sky Sports television.
Wolff said the team had made changes overnight and while Red Bull were still considerably quicker on the medium tyres they had less pace on the softs.
"George was saying the car is completely transformed the moment we put it on the softs, with the same setup. I think the difference was more than a second," he added.
"We don't think you can run it in the race but we will see tomorrow. Maybe we need to do something different."
