This win marked the fourth consecutive race win for the German driver, following three wins in a row to finish the 2015 F1 season.
It was a different story for Lewis Hamilton, as the reigning World Champ did not get the start he would have expected. His Mercedes struggled to take off - and quickly dropped into sixth position on the opening lap.
This poor start allowed Sebastian Vettel to jump into the lead, with Rosberg following closely behind in second place and the German pair began to pull away from the pack.
On Lap 19, a horrifying crash between Esteban Gutierrez and Fernando Alonso saw the race halted, as the race directors believed that a safety car was not enough to adequately clean up the wreckage caused by the crash.
When the race re-started, Vettel led the way - but a slow pitstop from the Ferrari team saw Vettel lose valuable seconds during a tyre change, which allowed Rosberg to snatch the lead from Vettel.
Ferrari's troubles got worse, when Kimi Raikkonen was forced to retire from the race from third place as flames spilled from his car's airbox.
After his poor start and the race stoppage, the Mercedes team decided to move Lewis Hamilton to a two-stop strategy for the race. This allowed him to overtake Vettel during a stop, Vettel was pushed into third place and Daniel Ricciardo of Red Bull finished fourth.
The Williams team of Felipe Massa finished the race in fifth, followed by Haas and Romain Grosjean - who secured sixth place in the American team's debut Formula 1 race.
Force India's Nico Hulkenberg, Williams' Valtteri Bottas and the Toro Rosso pair of Carlos Sainz and Max Verstappen rounded out the point scorers - with Renault narrowly missing the points in their return to F1.