Friday morning's opening 90-minute session was headlined by two red-flag stoppages as Williams driver Felipe Massa and Renault's Kevin Magnussen both suffered high-speed left-rear tyre failures while running on the same soft-compound rubber.
Felipe Massa set the tone for a bizarre morning by spinning off at turn four with a punctured left rear tyre - before astonishingly shredding another Pirelli on the same wheel, heralding red flags each time.
"Something is broke on the car," Massa observed with wry understatement, as officials halted the action to allow marshals to clear gravel and debris.
The problem seemed to be infectious with Kevin Magnussen forced to limp back to the pits on ruined rubber - also on his left rear - after Renault mechanics had warned him of possible brake issues.
The Swede grumbled about damaged suspension over the team radio as the red flags came out for the second time.
However, Formula One tyre supplier Pirelli said the problems were not caused by punctures; Williams technical head Pat Symonds blamed "wheel rim failure" for Massa's issues, while Renault suspects debris caused Magnussen's tyre to explode.
While Williams did not send its cars back out, there seemed to be no concern among other teams as they took to the track on the yellow-marked tyre for a frantic final eight minutes following the second stoppage.
ON THE TIMESHEETS
Rosberg's benchmark time of one minute 38.037 seconds was more than a tenth faster than second-placed team-mate Lewis Hamilton's best, but neither Mercedes driver had a straightforward session.
Rosberg, who leads Hamilton by 17 points in the standings and heads into the weekend aiming for his sixth consecutive win, limped home with engine issues at the end of practice.
Hamilton meanwhile, already carrying a five-place grid penalty due to a gearbox change, reported struggles with "locking" problems and spun twice at Turn 11.
Sebastian Vettel went third fastest for Ferrari, six-tenths slower than Rosberg, with Red Bull's Daniel Ricciardo fourth, more than a second adrift.
Fernando Alonso set the 12th fastest time on his return to track action after being forced to sit out the last race in Bahrain on doctors' orders due to injuries suffered in a crash in the season-opening Australian Grand Prix.
Alonso was also cleared to race on Sunday after undergoing further medical tests at the Shanghai circuit following the opening practice session on Friday.
The FIA said: "As a result of a medical examination undertaken following free practice one, the FIA F1 medical delegate, Professor Jean-Charles Piette, and the chief medical officer of the Chinese Grand Prix, Professor Shiyi Chen, have ruled that Fernando Alonso is fit to take part in all remaining sessions.”
However, the Spaniard would have to stop his car immediately in case of any abnormal symptoms, the FIA added.
Alonso sat out the previous race in Bahrain after failing a medical following an horrific accident in the March 20 season-opener in Melbourne that left him with fractured ribs and the risk of a collapsed lung.
1 Nico Rosberg (Germany) Mercedes – 1m38.037s
2 Lewis Hamilton (Britain) Mercedes - 1:38.183
3 Sebastian Vettel (Germany) Ferrari - 1:38.665
4 Daniel Ricciardo (Australia) Red Bull - 1:39.061
5 Kimi Raikkonen (Finland) Ferrari - 1:39.155
6 Daniil Kvyat (Russia) Red Bull - 1:39.625
7 Carlos Sainz Jr (Spain) Toro Rosso - 1:39.676
8 Jenson Button (Britain) McLaren - 1:39.974
9 Nico Huelkenberg (Germany) Force India - 1:40.169
10 Max Verstappen (Netherlands) Toro Rosso - 1:40.232
11 Sergio Perez (Mexico) Force India - 1:40.347
12 Fernando Alonso (Spain) McLaren - 1:40.538
13 Valtteri Bottas (Finland) Williams - 1:40.828
14 Romain Grosjean (France) Haas - 1:41.358
15 Marcus Ericsson (Sweden) Sauber - 1:41.393
16 Rio Haryanto (Indonesia) Manor - 1:41.614
17 Jolyon Palmer (Britain) Renault - 1:41.816
18 Pascal Wehrlein (Germany) Manor - 1:42.908
19 Felipe Nasr (Brazil) Sauber - 1:42.980
20 Kevin Magnussen (Denmark) Renault
21 Esteban Gutierrez (Mexico) Haas
22 Felipe Massa (Brazil) Mercedes
Original source: First Shanghai F1 session red-flagged twice