The Red Bull junior, who is trying to earn a Formula 1 graduation to Toro Rosso for next year, slipped from second to third at the start but took the lead during the mandatory pitstops.
With championship leaders Kevin Magnussen and Stoffel Vandoorne out front in the early laps, da Costa was giving chase and the Arden driver proved to be the quickest of the trio as they pulled away from the rest of the field.
He then waited for both of the McLaren F1 juniors to pit to give him clear track, and he emerged from his own stop just ahead of them.
Magnussen attacked on the outside into Turn 2 but da Costa held firm, and from there he drove away to a comfortable winning margin of more than six seconds.
The battle for second remained tight between DAMS racer Magnussen and Fortec's Vandoorne, but it was the championship leader who hung on to extend his gap back to the Belgian rookie in the points race to 46.
Behind the leaders, Nigel Melker capitalised on an early stop to vault up the order, converting 10th place on the grid into fourth by the finish.
He was made to work hard for that position by Nico Muller in the closing stages, but the race one winner could not quite find a way by and had to settle for fifth place.
Results - 28 laps:
Pos Driver Team/Car Time/Gap
1. Antonio F.da Costa Arden Caterham 45m40.876s
2. Kevin Magnussen DAMS +6.547s
3. Stoffel Vandoorne Fortec +7.230s
4. Nigel Melker Tech 1 +18.802s
5. Nico Muller Draco +19.128s
6. Andre Negrao Draco +22.016s
7. Marlon Stockinger Lotus +24.252s
8. Carlos Huertas Carlin +29.469s
9. Marco Sorensen Lotus +29.864s
10. Oliver Webb Fortec +31.073s
11. Norman Nato DAMS +44.567s
12. Sergey Sirotkin ISR +44.871s
13. Mikhail Aleshin Tech 1 +51.204s
14. Pietro Fantin Arden Caterham +51.949s
15. Matias Laine P1 +52.844s
16. William Buller Zeta Corse +53.228s
17. Lucas Foresti Comtec +54.154s
18. Zoel Amberg Pons +54.727s
19. Christopher Zanella ISR +55.918s
20. Jazeman Jaafar Carlin +58.007s
21. Yann Cunha AV Formula +1m07.540s
22. Carlos Sainz Jr. Zeta Corse +1m13.012s
Daniil Move Comtec 24 laps
Nikolai Martsenko Pons R 22 laps
Arthur Pic AV Formula 13 laps
Will Stevens P1 1 lap
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