Defender Dunk and winger Knockaert, both 25, have penned five-year deals with the Seagulls, while defender Duffy, also 25, has signed a new four-year deal.
Brighton manager Chris Hughton told the official club website: "Lewis, Shane and Anthony were key members of our promotion-winning side last season, and I fully expect them to be important members of the team once again this season.
"They're relishing the step up to the new level and they each have the capability to perform and excel in the Premier League - and they have certainly earned these new deals with their performances on the pitch.
"It's been a really straightforward process getting everything completed and I'm absolutely delighted that three key members of the squad have committed their futures to the Albion."
Brighton began the new Premier League season with a 2-0 defeat at home to Manchester City on Saturday.