Rosberg, who won the season opening race in Australia two weeks ago, clocked a best time of one minute, 39.909 seconds in the second session at a steamy, slippy Sepang circuit, where track temperatures reached 50 degrees Celsius, testing the cooling systems on the new V6 turbo engines to the max.
Rosberg's team mate Lewis Hamilton had clocked the best time of 1:40.691 in the opening session despite sliding off the track earlier on Friday, but the Briton was only fourth in the second with a 1:40.051 after more grip issues.
The 2008 world champion complained on the team radio after his first venture into the gravel that the circuit was "like driving on marbles" with less downforce and more torque and power on the new cars taking some getting used to.
The Spanish double world champion had led the timesheets in the opening half of the first session before making an error and spinning at turn eight and then concentrated on system and balance checks as his times slipped back.
World champion Sebastian Vettel was third quickest in the second session with a best time of 1:39.970 seconds but Red Bull team principal Christian Horner told Skysports that the team were having problems with a fuel sensor that required changing.
Fuel flow rates had led to Vettel's team mate Daniel Ricciardo being disqualified from his home grand prix in Melbourne last week, a verdict the team have appealed.
The Australian was seventh quickest in the second session on Friday and ended the day by taking a run over the grass.
He was behind Felipe Massa of Williams who also took a spin at turn eight, like his former Ferrari team mate Alonso, while Sauber's Adrian Sutil, Force India's Nico Hulkenberg and Jean-Eric Vergne in the Toro Rosso also had similar spin issues.
McLaren's Kevin Magnussen had an up-and-down day with his car stopping on the track at turn 15 in the opening session before the Danish rookie bemoaned oversteering in the second as he finished down the grid.
It was nothing compared to the problems of Lotus, however, with Pastor Maldonado not even making it out for the second session after engineers worked on his car which billowed smoke in the opening 90 minute run before he could register a time.
Romain Grosjean's Lotus faired little better with his car stopping at turn 10 also without him setting a lap before his second session was interrupted by another problem with his team telling him to bring the car back to the garage in second gear.
Japan's Kamui Kobayashi was also absent in the second session because of electronic control issues in his Caterham, while Max Chilton also missed most of the precious running time after going off the track after only six minutes.
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