Starting eight on the grid, Sutil passed both McLaren's Jenson Button (6th) and Ferrari's Fernando Alonso (7th) with opportunistic overtaking maneuvres at the hairpin en route to his fifth place finish to earn vital 10 points for his side.
His team-mate Di Resta too had a good day in office, as starting 17th, he moved up whopping eight places to drove home his VJM06 inside the top 10 bracket and collected two points in the process.
In a race marred by accidents, red flags and two safety car interventions, Rosberg drove flawlessly to claim only the second win of his career.
Reigning world champion Sebastian Vettel of Germany was second ahead of his team-mate Mark Webber to ensure a two-three finish for Red Bull. Mercedes' Lewis Hamilton claimed the fourth position.
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Jean-Eric Vergne of Toro Rosso finished eighth ahead of Di Resta, while Lotus' Kimi Raikkonen completed the top 10 chart.
The red flag came out with 30 laps to go in the 78-lap race when Williams' Pastor Maldonado was pushed into the wall by Max Chilton of Marussia.