In a session that started slowly on a damp track following a late morning downpour, the Mercedes driver topped the timesheets with a one minute, 36.877 lap as the leading drivers leapfrogged each other with a flurry of late fast times.
The Red Bulls showed that their poor performance in Friday's second session was a minor blip as world champion Sebastian Vettel and team mate Mark Webber clocked the next fastest times ahead of a resurgent Kimi Raikkonen.
Vettel finished 0.443 seconds behind Rosberg as the teams opted to put the cars in qualifying mode after it took 28 minutes of the hour-long session before anyone completed a timed lap.
Lewis Hamilton, who had dominated both of the Friday practice sessions, was less fortunate a day later when the Briton ran off into the gravel on his first timed lap and returned to the pits with shredded tyres.
The 2008 world champion managed just one more quick lap in the final 10 minutes but was still 0.899 seconds off the pace set by Rosberg down in ninth place.
Raikkonen, fitted with a new gearbox that will cost him five places on the starting grid, gave an indication that the Lotus car will be competitive in Sunday's race, his form backed up by team mate Romain Grosjean, who was just behind him in fifth.
Jenson Button, who won the season-opener in Melbourne last week, was sixth fastest in the other McLaren, ahead of an impressive Pastor Maldonado in a Williams and Michael Schumacher's Mercedes.
Ferrari were again unable to keep pace with the leaders and could struggle to make the latter stages of qualifying later on Saturday as Fernando Alonso was only able to manage a 13th fastest time, five places ahead of team mate Felipe Massa.