The Wolfpack set up the winning play after a timeout with 7.5 seconds to go.
Brown also hit two free throws with 14 seconds left to cut Clemson's lead to two. The Tigers (12-11, 4-7) led for almost the whole game, but Milton Jennings missed the front end of a 1-in-1 with 12.3 seconds left.
Richard Howell led N.C. State with 16 points and 11 rebounds. C.J. Leslie added 12 points and 10 rebounds for the Wolfpack, who were the preseason pick to win the ACC before losing three in a row -- a streak that started when Brown left a 58-55 loss to Virginia with the hurt ankle in the first half. N.C. State plays just one team in the ACC top four the rest of the way, giving them a chance to climb back toward the top of the league.
Freshman Jordan Roper led Clemson with a career-high 17 points in his first ACC start. K.J. McDaniels scored 12 points and Devin Booker added 10 points and six rebounds for the Tigers.
Clemson held the ACC's best shooting team to just 38 percent shooting (23-of-61) from the field, but the Tigers had 17 turnovers.
Wood hit a 3-pointer to open the game, but Clemson quickly took the lead back. The Wolfpack took their second lead of the game on Howell's layup with nine minutes to go, but McDaniels hit a 3 and Booker make a basket to put the Tigers in the lead again.
Rod Hall would score six of the next eight points for Clemson, including a drive that put the Tigers ahead 57-53 with 19.3 seconds left. Brown drove the ball on N.C. State's next possession and hit both foul shots. Jennings' missed free throw then set up the winning basket.
Roper scored Clemson's first 10 points of the second half to reach his career high.