The Red Bull driver started the race second on the grid, but down the first straight he overtook Lewis Hamilton, who had begun in pole position. Vettel's teammate Mark Webber also managed to negotiate his way beyond the Brit.
Vettel came in early for a change of tyres, which cost him his lead. However, when his fellow competitors followed suit, he was able to regain his earlier advantage.
The remainder of the race went by without incident for the 26-year-old that allowed him to take the chequered flag.
Result in full:
1. Sebastian Vettel (Red Bull)
2. Kimi Raikkonen (Lotus)
3. Romain Grosjean (Lotus)
4. Fernando Alonso (Ferrari)
5. Lewis Hamilton (Mercedes)
6. Jenson Button (McLaren)
7. Mark Webber (Red Bull)
8. Sergio Perez (McLaren)
9. Nico Rosberg (Mercedes)
10. Nico Hulkenberg (Sauber)
11. Paul Di Resta (Force India)
12. Daniel Ricciardo (Toro Rosso)
13. Adrian Sutil (Force India)
14. Esteban Gutierrez (Sauber)
15. Pastor Maldonado (Williams)
16. Valtteri Bottas (Williams)
17. Charles Pic (Caterham)
18. Giedo van der Garde (Caterham)
19. Max Chilton (Marussia)
Not classified: Jean-Eric Vergne (Toro Rosso), Jules Bianchi (Marussia), Felipe Massa (Ferrari)