Now the German hopes he can gain further ground on Mercedes teammate Lewis Hamilton at his favourite Monaco track in two weeks.
Rosberg beat Hamilton for the first time this season, with Ferrari's Sebastian Vettel placing third.
The morale-boosting win was Rosberg's first since the Brazilian GP — the penultimate race of the last season — which the German driver also won from pole. It also gives him a sense of momentum heading into Monaco, where Rosberg, the son of former world champion Keke Rosbger, grew up. He won the showcase race from pole last year, and then went on to win in Austria and Germany.
A third straight win at Monaco would dent Hamilton's 20-point lead.
"I was able to control the pace and I never felt in danger throughout the whole race," Rosberg said. "It's still early days in the season so it's good to close the gap to Lewis. I will continue to push hard, starting with a home race for me in Monaco."
Hamilton, the defending F1 champion, has won three of five races this season, with Vettel taking the Malaysian GP in March.
"I had a good start, getting past Lewis," Vettel said. "But unfortunately Mercedes were just too quick."
McLaren's poor season continued as two-time F1 champion Fernando Alonso retired just short of halfway with faulty brakes — on the same track where he last won a race two years ago with Ferrari.
Hamilton has finished in the top two for 12 straight races since retiring at last season's Belgium GP in August. Dominant Mercedes has finished 1-2 in three of five races this campaign.
"Everyone brought upgrades here and we're still much faster," Rosberg said.
As Rosberg milked the applause after the race, Hamilton walked up to him, patted him on the back and then shook his hand firmly.
There was no Spanish driver in genuine contention and little suspense, either.
With 19 of the past 25 winners here starting from pole, the circuit is arguably the hardest to overtake on in F1. Rosberg finished 17.5 seconds clear of Hamilton and some 45.3 ahead of Vettel.
"I think I'm in the fight," Vettel said. "I'm pretty confident we will get closer again pretty soon. I'm quite confident that in the next couple of races we should be stepping up our game."
Although the 730-meter straight to the first turn offered Hamilton the chance to apply instant pressure, Rosberg got away well. Hamilton stuttered as Vettel overtook him and he only just held off the Williams of Valtteri Bottas heading into the first corner. Bottas finished fourth and Ferrari's Kimi Raikkonen was fifth.
"It's been a long time since I had such a bad start," Hamilton said. "I tried my best to recover."
It wasn't Hamilton's day, as his first pit stop on lap 14 for a new set of medium tires took 5.3 seconds because a mechanic appeared not to get the left rear wheel on cleanly. Vettel's first stop was an extremely fast 2.3 seconds.
"I had a long pit stop and I had to do it all again," Hamilton said. "But fortunately at the end it was enough (to catch Vettel)."
Rosberg came in for his first tire change on lap 16 — at a marginally slower 2.5 seconds — while Raikkonen stayed out in front.
Hamilton was urged by his race engineer to push more strongly to overtake Vettel, to which Hamilton replied: "I can assure you that's pretty much impossible to do, you're going to have to come up with another plan."
The plan chosen was a three-stop strategy.
Alonso overshot his stop as he entered the pits, sending a front jack flying which missed the mechanic nearby.
Nothing was troubling Rosberg as he extended his lead over Vettel to 10 seconds by halfway. Hamilton switched to hard tires after 33 of 66 laps.
Vettel made his second stop on lap 40 while Rosberg made his second with 20 laps remaining, coming out just behind Hamilton as the British driver led for the first time.
Nearing the end of lap 51, Hamilton came in for his final change, getting back onto medium tires, but Rosberg moved ahead and was too far away to catch.