Rosberg set a quickest time of 1 minute, 55.409 seconds to lead Lewis Hamilton of McLaren and Schumacher by just under half a second after two sessions.
Schumacher, a seven-time champion racing for the first time in three years, said he needed to raise his game and shake off the rust in time for Saturday's qualifying.
"It's a bit too much for my standards, so I gotta raise my game a bit and I'm sure I'm going to," said the 41-year-old German, who skidded off the track at one point during the first session.
"It has been fun but I certainly feel a little bit rusty, especially on the (qualifying lap) issue. I'll just use the rest of the weekend to tweak out a few little things." Defending champion Jenson Button was fourth for McLaren, ahead of Red Bull driver Sebastian Vettel, who was just over 1 second off Rosberg's pace.
Felipe Massa finished 1.1 seconds behind and Ferrari teammate Fernando Alonso was 1.3 seconds back as the preseason's top four now wait on qualifying to reveal the teams' form for the season.
Vettel said McLaren and Ferrari looked the most competitive, while Alonso and Hamilton remained uncommitted.
"I have no idea," Alonso answered when asked if his Ferrari was capable of putting him on pole position for Sunday's race. "It's still completely unknown for everybody. The four big teams, any of them can be quick tomorrow and be on pole." Nico Hulkenberg of Williams was just over a second off the pace for sixth, while Adrian Sutil was also in that range as Force India continued to display the strong pace that carried it to points in the home stretch of last season.
Hot temperatures at the desert track came into play and accelerated tire degradation.
Drivers will need to carefully manage tires on heavy cars as a result of new rule changes that did away with refueling in the upcoming season.
"It's a bit of a dog to drive it on a heavy fuel tank," Hamilton said of the heavier set-up. "It's like driving a bus. (The car) doesn't stop as well." The drivers were also unhappy about the new-look track, which has added eight new corners to slow the cars.
"It's hard to concentrate on the next corner with your head bouncing all over the place. It's tricky," Button said of the new section. "It's a good place to lose a lot of time so you have to be careful. It doesn't help overtaking in any way." Button said he was "reasonably happy" with his car and his new start at McLaren after winning the title with Brawn GP - now Mercedes - last year.
"I've chosen my new challenge and that is to race here. I think I needed that challenge after winning the championship," the Briton said. "It's not that I'm not hungry, I'm so hungry." While the top teams prospered, the rookie teams continued to struggle at the back of the grid with Bruno Senna losing a piece of his rear tire on the final lap in his Hispania Racing car.
Heikki Kovalainen was the top driver among the new teams with a best lap of 2:00.873 for Lotus, which finished ahead of Virgin and HRT.
Senna, nephew of three-time champion Ayrton Senna, managed 20 laps over the two sessions with a best time of 2:06.968 - nearly 12 seconds off the pace.
Teammate Karun Chandhok did not test because his car was still not ready.
"We made history for the team today," Senna said as the Spanish team arrived at the season-opening race without the benefit of preseason testing.
