The German started the race second on the grid as a result of yesterday's qualifying, but he managed to gain the lead from Lewis Hamilton during the first lap, having got into the Mercedes driver's slip stream.
From that moment on Vettel held on to first spot, despite some late pressure from Ferrari's Fernando Alonso.
The Spaniard battled on for second spot, while Briton Hamilton took the final podium place.
Result in full:
1. Sebastian Vettel (Red Bull)
2. Fernando Alonso (Ferrari)
3. Lewis Hamilton (Mercedes)
4. Nico Rosberg (Mercedes)
5. Mark Webber (Red Bull)
6. Jenson Button (McLaren)
7. Felipe Massa (Ferrari)
8. Romain Grosjean (Lotus)
9. Adrian Sutil (Force India)
10. Daniel Ricciardo (Toro Rosso)
11. Sergio Perez (McLaren)
12. Jean-Eric Vergne (Toro Rosso)
13. Nico Hulkenberg (Sauber)
14. Esteban Gutierrez (Sauber)
15. Valtteri Bottas (Williams)
16. Giedo van der Garde (Caterham)
17. Pastor Maldonado (Williams)
18. Jules Bianchi (Marussia)
19 Max Chilton (Marussia)
Not classified: Paul Di Resta (Force India), Kimi Raikkonen (Lotus), Charles Pic (Caterham)