The Mercedes driver took the opening race of the season in Melbourne last month and was fastest man in the pack again Sunday -- but he was given a helping hand when misfortune befell likely title rivals Lewis Hamilton and Sebastian Vettel.
Ferrari's Vettel was forced to withdraw on the pre-race formation lap with smoke billowing from his engine.
Rosberg's Mercedes teammate Hamilton, meanwhile, stuttered from pole position on the grid before colliding with Valtteri Bottas of Williams at turn one.
Hamilton's nightmare start saw his car suffer bodywork damage as he dropped back to seventh position.
Naturally, Rosberg needed little encouragement to take the lead, a position the German driver would not relinquish.
"It's been an awesome weekend," Rosberg said shortly after stepping down from the podium. "The key was the start. I got a great getaway and from there I was just trying to control the race."
Vettel's Ferrari teammate, Kimi Raikkonen, finished second 10.2 seconds behind Rosberg while Hamilton would battle back to finish third.
The Briton later described the result as "damage limitation" given his troubles at the start to the race.
Vettel, meanwhile, revealed his frustration at the "very sudden" nature of the incident that ended his race in comments carried by the AFP news agency. But remained confident it was not indicative of wider problems.
"I think we have reason to be confident (for the remainder of the season) but it caught us by surprise today," he added.
Hamilton is now second in the driver's title race, 17 points behind Rosberg who has a maximum 50 points.
Three-time world champion, Hamilton, remains nine points clear of Daniel Ricciardo who lies third in the overall standings. Red Bull's Ricciardo finished fourth in Bahrain Sunday, one place ahead of Romain Grosjean of the American Haas team.
Max Verstappen of Torro Rosso claimed sixth spot ahead of the second Red Bull driven by Daniil Kvyat.
Felipe Massa of Williams, Bottas in the second Williams and Belgian debutant Stoffel Vandoorne took the final points positions, finishing eighth, ninth and tenth respectively.
Vandoorne will be especially delighted with his showing given the fact he was filling in for former F1 champion Fernando Alonso who has yet to fully shake off the effects of a horror crash in Melbourne