Hamilton, who also complained of gear shift irregularities, lapped in 1m 39.085s to Rosberg's 1m 39.088s. The German had also warned of gear shift problems, only to later admit they were of his own inadvertent making.
Ferrari's Fernando Alonso was the Silver Arrows' closest challenger on 1m 40.189s, just over one second down on Hamilton.
Daniel Ricciardo had a better session relative to FP1 and captured fourth for Red Bull on 1m 40.390s, while Felipe Massa wheeled his Williams round in 1m 40.457s. Kimi Raikkonen was sixth in the second Ferrari on 1m 40.543s, but also complained of clutch slip. Daniil Kvyat remained in striking distance with 1m 40.631s in the lead Toro Rosso, just ahead of the McLarens of Kevin Magnussen and Jenson Button on 1m 40.641s and 1m 40.698s respectively.
Force India's Nico Hulkenberg and Williams' Valtteri Bottas were the last two drivers to break the 1m 41s barrier, posting 1m 40.800s and 1m 40.828s respectively.
Romain Grosjean was another to enjoy improved form in FP2, fighting back from an early high-speed half-spin at Turn 4 to put his Lotus 12th on 1m 41.054s. The Frenchman was chased by compatriot Jean-Eric Vergne's Toro Rosso on 1m 41.110s, Sergio Perez's Force India on 1m 41.123s, Pastor Maldonado's Lotus on 1m 41.158s, and the Saubers of Adrian Sutil and Esteban Gutierrez on 1m 41.332s and 1m 41.420s.
After losing time in the pits at the start of the session, Red Bull's Sebastian Vettel - who has claimed pole in the last two races in Austin - was 18th and last, with 1m 43.980s. However the German, who will start Sunday's race from the pit lane after using his sixth power unit of the season, appeared to concentrate on race simulation runs.
Aside from Grosjean, Maldonado provided drama with spins in Turns 1 and 19, while Massa lost the rear of his Williams at Turn 1.