Button, whose last pole position came at the 2009 Monaco Grand Prix in his title-winning year with Brawn GP, could still secure the team's 150th pole.
Hamilton, winner in China in 2011 and also quickest in Friday morning's session, lapped the Shanghai circuit in a best time of one minute 35.940 seconds with Button 0.123 seconds slower.
Nico Rosberg was third fastest for Mercedes with seven times world champion team mate Michael Schumacher, whose 91st and last win was in China with Ferrari in 2006, fourth. Rosberg was 0.449 slower than Hamilton.
Australian Mark Webber lapped fifth quickest with double champion Sebastian Vettel ninth in the other Red Bull.
Ferrari showed no signs of shaking off their troubles with championship leader Fernando Alonso 15th and Brazilian Felipe Massa 18th.