Brown's clinching foul shots gave him 12 points for the game and he also added seven assists and six rebounds for the 11th-seeded Wolfpack (24-12).
C.J. Williams, Scott Wood and C.J. Leslie each supplied 14 points for N.C. State, which gained the Sweet 16 for the first time since 2005.
The Hoyas (24-9) were led by Hollis Thompson with 23 points and five board.
Jason Clark added 10 points for third-seeded Georgetown.