Hamilton was quicker in both sessions, by 0.133 seconds in the first and 0.083secs in the second.
The two traded fastest times throughout the day as their season-long battle comes to a nail-biting climax.
Hamilton leads Rosberg by 17 points and must finish second in Sunday's race, if the German wins, to be champion.
The battle between the two looks poised to be as close here as it has been all season.
On their qualifying-simulation runs on the super-soft tyre on which all will qualify, Hamilton was 0.144secs quicker than Rosberg on their first laps before Rosberg closed the gap slightly on their second.
A tense battle for pole position looks in store for Saturday, followed by an equally nail-biting race, although Hamilton appeared to have a distinct advantage over his team-mate on the race-simulations laps in the final part of the session.
The two Mercedes were well clear of the opposition - third-fastest man Kevin Magnussen's McLaren was 0.782secs off the pace.
The Dane, who set his time using McLaren's standard front wing rather than the new design brought to this race with a view to 2015, was 0.064secs quicker than Red Bull's Sebastian Vettel.
Williams's Valtteri Bottas was 0.11secs further behind in fifth, ahead of Red Bull's Daniel Ricciardo and Ferrari's Kimi Raikkonen, whose team-mate Fernando Alonso failed to set a time because of an electronics failure.
McLaren's Jenson Button was eighth fastest after missing the entire first session with a suspension problem and and the first half of the second with a hydraulics issue.
Toro Rosso's Daniil Kvyat and Williams's Felipe Massa completed the top 10.
Lotus's Romain Grosjean will be hit with a 20-place grid penalty for changing his engine and taking a sixth power-unit.
If he cannot take it all in one go - which he will not as he will not be on pole - officials have come up with a series of time penalties he will have to serve in the race depending on where he qualifies.