The Briton, who was top in both of Friday's sessions, completed 12 laps and was 0.115 seconds quicker than team mate Nico Rosberg as the pair finished one-two for the third practice in a row at the Sakhir desert circuit.
Hamilton, the 2008 champion, can complete another hat-trick in qualifying for the third race of the season after taking pole position in Australia and Malaysia.
While Mercedes were again the class act in the field on a clear and hot afternoon, Red Bull's quadruple world champion Sebastian Vettel ended up 21st of 22 drivers on the timesheets after spinning off and into the gravel.
"I spun on the exit of Turn Two and the engine went off immediately," said the German, who walked back into the paddock before the session had ended.
Mexican Sergio Perez was third fastest in a Force India with Valtteri Bottas fourth for Williams, who left it late to get their cars out, ahead of Brazilian team mate Felipe Massa and McLaren's Jenson Button.
The top six drivers were all in Mercedes-powered cars.
The best of the rest was Ferrari's Fernando Alonso who was seventh fastest.
Qualifying will be in far cooler conditions, with Sunday's race switching to a day-to-night format under floodlights for the first time. Track temperatures in final practice were around 35 degrees celsius.
Rosberg leads Hamilton by 18 points after two races, with the Mercedes drivers on one win apiece.
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