The Briton, 14 points behind championship-leading team mate Nico Rosberg after 10 races but favourite for Sunday, lapped the Hungaroring circuit with a best time of one minute 24.048 seconds.
For the third session in a row, Rosberg was second on the timesheets, this time 0.047 slower.
Hamilton has won in Hungary for the last two years and four times in total, more than any other current driver and a record he shares with Michael Schumacher.
The Briton, who suffered a brake disc failure in qualifying at the German Grand Prix last weekend and raced from 20th through to third, will be hoping to carry the momentum through to reel in Rosberg before the August break.
Red Bull's quadruple world champion Sebastian Vettel was third fastest, 0.407 off the pace, with Australian team mate Daniel Ricciardo fourth on another hot but cloudy day in Budapest.
Finland's Valtteri Bottas, who has been on the podium in the last three races, was fifth for Williams ahead of Ferrari's Fernando Alonso and Kimi Raikkonen.
(Reporting by Alan Baldwin; Editing by John O'Brien)
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