The pair were split by just 0.115s, as the Englishman continued to lead with 1m 35.324s and the German chased him hard with 1m 35.439s.
The big surprise was Sergio Perez's smooth run to third for Force India which made him the only other runner to dip beneath 1m 36s. The Mexican's 1m 35.868s left him just 0.544s shy of Hamilton, and six-tenths up on team mate Nico Hulkenberg, who managed 1m 36.455s in the sister VJM07.
In between them Valtteri Bottas vaulted to fourth on 1m 36.116s and Felipe Massa to fifth on 1m 36.364s, as both Williams drivers surged up the order following a switch to the softer Pirelli tyres. They thus displaced Jenson Button, who continued to outpace McLaren team mate Kevin Magnussen; the Englishman was sixth with 1m 36.394s, the Dane 11th on 1m 36.822s.
Ferrari lost pace relative to Friday practice, with Fernando Alonso seventh on 1m 36.454s - ahead of Hulkenberg - and Kimi Raikkonen 10th on 1m 36.772s. Toro Rosso's Daniil Kvyat again demonstrated his ability to go out and get a time straight away on the medium tyres, before improving to 1m 36.680s on the softs for ninth.
The big drama of the session concerned Red Bull. Daniel Ricciardo was only 13th on 1m 37.119s, behind stable mate Jean-Eric Vergne in the other Toro Rosso on 1m 37.030s, while Sebastian Vettel was down in 21st on 1m 39.225s after spinning into the gravel exiting Turn 2 before he even got a run on the soft rubber.
Esteban Gutierrez was Sauber's best runner in 14th on 1m 37.325s, which put him ahead of team mate Adrian Sutil who managed 1m 38.089s, while Kamui Kobayashi gave Caterham heart with the 16th fastest time of 1m 38.400. Right behind him, however, was Marussia's Jules Bianchi on 1m 38.736s, Pastor Maldonado's ill-handling Lotus on 1m 38.880s and Marcus Ericsson in the second Caterham on 1m 38.971s.
Romain Grosjean didn't better 1m 39.208s for Lotus as he too struggled with the E22's handling, and Max Chilton brought up the rear on 1m 39.597s in the second Marussia.
Thus the scene is set for qualifying, which begins once darkness has fallen at 1800 hours local time. All things being equal Mercedes look heavy favourites for pole, but the second row of the grid looks like being an incredibly tight fight between Force India, Williams, McLaren and Ferrari.