The Mercedes duo, who took pole position in all but one of last season's qualifying sessions and won 16 of the 19 races, were dominant in first and second practice for Sunday's Australian Grand Prix.
Rosberg, who won last year's GP at Albert Park, was fastest around the Melbourne street circuit on Friday, finishing 0.1 second ahead of Hamilton with Sebastian Vettel taking third spot for his new team Ferrari -- the German four-time world champion finished 0.715 seconds off the pace set by his compatriot.
Vettel's Finnish teammate, Kimi Raikkonen was fourth, 1.1 seconds behind the lead with Williams' Valtteri Bottas and Daniel Kvyat, who was making his debut for Red Bull since his switch from Toro Rosso, finishing fifth and sixth respectively.
"It was great to be back in the car at this awesome track," Rosberg said, the official Formula One site reported
"Today we have the evidence that our Silver Arrow is quick again and it was a great start for the team," he added.
"It seems again that it's very close between Lewis and me and he is a great driver, so I need to nail the setup every time to come out on top. This year will be a big battle again against him, I'm sure. I'm looking forward to the first weekend of the new season with all the great fans out there."
Hamilton, who was forced to retire from last year's race with engine trouble, was satisfied with his pace.
"It feels great to be back on track and back into a race weekend. In general it's been a good first day," Hamilton said.
"Today seemed to confirm that we have pretty good pace. But there are still other quick cars out there and we can't go into tomorrow's sessions not thinking that they will be close."
The opening day's racing was somewhat overshadowed by an ongoing dispute between Sauber and the Swiss team's 2014 reserve driver Giedo van der Garde.
The 29-year-old Dutchman recently started legal proceeding against the Swiss team claiming they had reneged on a promise to make him one of the lead drivers for the 2015 season.
Van der Garde won the case held in a Swiss court earlier this month, with the decision being upheld by Supreme Court of Victoria in Australia on Tuesday after Sauber had appealed the original ruling.
During practice Van der Garde could be seen in the Sauber garage wearing his race overalls, but he did not make an appearance on track as Marcus Ericsson and Felipe Nasr completing both practice sessions.
Following the initial court ruling, team principal Monisha Kaltenborn said that changing drivers hours before a Grand Prix could be dangerous.
"What we cannot do is jeopardize the safety of our team, or any other driver on the track, by having an unprepared driver in a car that has now been tailored to two other assigned drivers," she said, Formula1.com reported.
Brazilian Nasr was the highest placed of the two finishing 11th while Swede Marcus Ericsson was 15th.
Elsewhere there was also a uncertain start for McLaren who finished way down the pecking order.
Jenson Button was 13th, almost four seconds off the pace for the CNN-sponsored team while teammate Kevin Magnussen, who was deputizing for the absent Fernando Alonso
, was 16th following second practice.
Local favorite Daniel Ricciardo completed just nine laps of practice after his Red Bull suffered engine failure.
Qualifying for Sunday's race gets underway on Saturday.