Button, the reigning champion and last year's winner with Brawn at the undulating anti-clockwise Istanbul Park circuit, set the pace in the afternoon with a time of one minute 28.280 seconds.
That time was faster than Sebastian Vettel's 2009 pole position for Red Bull of 1:28.316.
Hamilton, the 2008 champion, had earlier led a McLaren one-two with a best lap of 1:28.653, with Button 0.962 slower in second place.
Red Bull's championship leader Mark Webber was second in the afternoon, but stopped on track five minutes from the end with a smoking car.
Vettel, fifth in the morning, was third.
Friday was the German's first chance to try out a different chassis, dubbed 'Randy Mandy' and used previously only in pre-season testing, at a grand prix weekend after a defect was discovered in the car he had used for the past six races.
Friday practice is more morale-boosting than indicative of true performance, although Webber warned on Thursday that the McLarens could be a real threat.
"We saw in Barcelona that things were a little bit different," the Australian, who is level with Vettel on 78 points after six races, reminded reporters.
"Lewis was our closest competitor in that Grand Prix, so you can argue that if we had a Turkish Grand Prix after Barcelona, you might say that the McLaren might be the guys that might be our challengers here.
"But we're also mindful of the fact that Ferrari, and also if Mercedes have a clean weekend, there's lots of guys that can come towards us, so we're definitely not taking anything for granted," he added.
Webber is going for a third win in a row after his victories in Spain and on the winding streets of Monaco.
Ferrari's Fernando Alonso, third in the championship ahead of his team's 800th race, was ninth and fifth respectively.
Force India's German Adrian Sutil had the only accident of the morning session, the German losing control through the difficult Turn Eight in the closing minutes and spinning into the barriers.
Brazilian Bruno Senna sat out that practice for HRT, his place going to test driver Sakon Yamamoto. The Japanese was 7.4 seconds off the pace and more than a second slower than Indian Karun Chandhok in the other HRT.
