The Harry Potter star was honoured with the PPG Award for Best Performance in a British Feature Film trophy for his role in the new movie, which sees Rhys Ifans portray notorious drug smuggler Howard Marks.
The festival jury, which included Sir Patrick Stewart, director Mike Hodges and actress Britt Ekland, called Thewlis' performance as Irish Republican Army activist Jim McCann "energetic and electrifying".
Thewlis said, "This is a thrill and totally unexpected, and made all the more special by being honoured by one of my favourite cities in the world."
The Best New British Feature Film prize went to Skeletons, which features Thewlis' Harry Potter co-star Jason Isaacs, while America Ferrera's The Dry Land was named Best International Feature.
Robert Duvall's dark comedy Get Low took the 2010 Standard Life Audience Award and Gareth Edwards won the Moet New Directors Award for Monsters. The Best Feature Documentary Award went to The Oath.
Oscar-winning actress Tilda Swinton was on hand to help present the awards in her role as festival patron.