It was not all plain sailing for the Silvers Arrows however, as Rosberg suffered a glazed brake disc and Hamilton - who was only fifth fastest on Pirelli's medium tyre - spun when he lost the rear of his Mercedes under braking for Turn 12.
In the end though Hamilton's late 1m 37.107s on the soft tyre obliterated Massa's fastest time of 1m 38.214s on similar rubber, which had in turn beaten Valtteri Bottas's 1m 38.437s in the second Williams.
Due to his brake issues, it wasn't until the final minutes that Rosberg also vaulted the Williams duo, slotting into second with 1m 37.992s, which he later trimmed by a whisker to 1m 37.990s.
Fernando Alonso hung on for fifth for Ferrari with 1m 38.727s, as Red Bull's Daniel Ricciardo fell back to sixth on 1m 38.927s.
Nico Hulkenberg and Adrian Sutil took surprise seventh and eighth places for Force India and Sauber respectively, with 1m 38.960s and 1m 39.000s, leaving Kimi Raikkonen in the second Ferrari ninth on 1m 39.143s, ahead of the McLarens of Jenson Button and Kevin Magnussen on 1m 39.241s and 1m 39.335s.
Lotus were much improved, with Pastor Maldonado 12th on 1m 39.448s and Romain Grosjean 13th on 1m 39.561s. Sergio Perez took 14th for Force India with 1m 39.582s, and Daniil Kvyat was only 15th in the lead Toro Rosso on 1m 39.688s. Esteban Gutierrez was next on 1m 40.208s in the other Sauber, ahead of Jean-Eric Vergne's Toro Rosso on 1m 41.443s.
Sebastian Vettel was last on 1m 43.765s as he continued to focus on race work following confirmation that he will start Sunday's race from the pit lane after using his sixth power unit of the season in Austin.