The McLaren junior was up to eighth - and on the tail of title rival Stoffel Vandoorne - after just two racing laps following a safety car start, and from there he methodically picked his way through the rest of the runners to climb to second place.
Vandoorne was able to follow him through the field for a while after the two swapped places, but Magnussen's quick work of getting past Negrao, Sergey Sirotkin and Will Stevens proved decisive in creating a gap back to his main rival.
Sirotkin also found a way past Negrao to take the final spot on the podium, while Vandoorne managed to climb to fourth having started 11th.
Polesitter Negrao's race ended in disappointment, as he spun out of fifth place at the end of the penultimate lap having battled electrical gremlins for much of the race.
That handed a top five finish to Mikhail Aleshin, who had been spun out of third early on when he was tagged by Antonio Felix da Costa at Turn 5 on the first racing lap.
Da Costa, who had started fourth, lost any hope of a good result in the collision, and he was forced to retire a few corners later with damage to the front left of his car.
Race 1 - 22 laps:Pos Driver Team Time/Gap
1. Nico Muller Draco 47m59.721s
2. Kevin Magnussen DAMS +26.200s
3. Sergey Sirotkin ISR +30.078s
4. Stoffel Vandoorne Fortec +31.265s
5. Mikhail Aleshin Tech 1 +34.482s
6. Nigel Melker Tech 1 +37.447s
7. Carlos Sainz Jr Zeta Corse +38.828s
8. Will Stevens P1/Strakka +50.125s
9. Arthur Pic AV +51.440s
10. Matias Laine P1/Strakka +58.962s
11. Nikolay Martsenko Pons +59.787s
12. Marco Sorensen Lotus +1m01.575s
13. Marlon Stockinger Lotus +1m05.320s
14. Lucas Foresti Comtec +1m16.056s
15. Norman Nato DAMS +1m18.318s
16. Oliver Webb Fortec +1m24.834s
17. Carlos Huertas Carlin +1m42.507s
18. Daniil Move Comtec +1m47.406s
19. Zoel Amberg Pons +1m52.973s
20. Jazeman Jaafar Carlin +1m54.582s
21. Andre Negrao Draco +2 laps
Yann Cunha AV 17 laps
Christopher Zanella ISR 12 laps
Will Buller Zeta Corse 6 laps
Antonio Felix da Costa Arden Caterham 5 laps
Pietro Fantin Arden Caterham 5 laps
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