From fourth on the grid, Lancaster made a phenomenal start as those ahead of him all suffered wheelspin.
Despite a scare when the safety car came out, to allow Daniel Abt's spun ART car to be recovered from the middle of the track at Farm, Lancaster drove a superbly-judged race to win by 6.5s.
It was series newcomer Hilmer Motorsport's second victory of the season.
Rio Haryanto finished second for Addax, well clear of ART's James Calado, who came through from eighth on the grid to finish on the podium. He had to hold off poleman Julian Leal for the majority of the race distance.
Sam Bird passed Russian Time team-mate Tom Dillmann for fifth to aid his championship challenge, while Dillmann did well to hold off a charging Felipe Nasr. Apart from Lancaster, the Brazilian was the star of the race, charging from 25th to seventh.
Marcus Ericsson finished eighth, just holding off Alexander Rossi.
Silverstone sprint race results
1. Jon Lancaster Hilmer Motorsport
2. Rio Haryanto Barwa Addax Team
3. James Calado ART Grand Prix
4. Julian Leal Racing Engineering
5. Sam Bird RUSSIAN TIME
6. Tom Dillmann RUSSIAN TIME
7. Felipe Nasr Carlin
8. Marcus Ericsson DAMS
9. Alexander Rossi EQ8 Caterham Racing
10. Stefano Coletti Rapax
11. Adrian Quaife-Hobbs MP Motorsport
12. Kevin Ceccon Trident Racing
13. Rene Binder Venezuela GP Lazarus
14. Mitch Evans Arden International
15. Fabio Leimer Racing Engineering
16. Simon Trummer Rapax
17. Fabrizio Crestani Venezuela GP Lazarus
18. Daniel De Jong MP Motorsport
19. Stéphane Richelmi DAMS
20. Sergio Canamasas EQ8 Caterham Racing
21. Jake Rosenzweig Barwa Addax Team
- Sports & Recreation
- Motor Racing
- James Calado
- Hilmer Motorsport
- Tom Dillmann
- Julian Leal