Having already topped the timesheets in both P1 and P2 in Austin, the Briton laid down another marker ahead of qualifying later on Saturday by finishing more than eight tenths ahead of fellow Mercedes man Rosberg in second.
In a far from ideal session for the German, he first suffered glazed brake discs and was then held up before starting a flying lap, eventually posting a time of one minute 37.990 seconds.
The Mercedes pair were the only men to dip into the 1min 37s, with Williams' Felipe Massa (1:38.214) and Valtteri Bottas (1:38.437) back in third and fourth.
Fernando Alonso - looking to end Ferrari's near 18-month wait for a grand prix win - briefly led the session after making his mark on the softer tyres, but he ultimately ended in fifth in a time of 1:38.727.
For Hamilton - who holds a 17-point lead over his team-mate in the title race - it represented another show of force as he seeks a fifth consecutive race win.
But his session was not without incident, the 29-year-old falling foul of Turn 12 on his second proper lap out of the garage as he spun.
Rosberg followed him off track soon afterwards - also overcooking his entry into Turn 12 - before another error heading into Turn 15 saw him mount the kerb.
At one stage, it looked as though the German may struggle to post a competitive time, but late in the session he finally found his rhythm - although, having been held up by Sebastian Vettel prior to starting a late flying lap, he still ended well short of Hamilton's pace.
