The preseason league favorites were 7 of 8 from the free-throw line in the final minute of OT to win their second straight.
After the teams traded turnovers, Tyler Lewis hit two free throws with 51.8 seconds left to give N.C. State an 85-84 lead.
Brown sandwiched two sets of two made free throws around a critical steal from Green with about 20 seconds left.
Wood finished with a season-best six 3-pointers and was one point shy of the season high he set two months ago against St. Bonaventure. Brown was strong in his first start since suffering an ankle injury during a Jan. 29 loss at Virginia -- the first of three straight losses that knocked the Wolfpack from the national rankings.
Lewis finished with 13 points and fellow freshman T.J. Warren had 12 for N.C. State.
Marshall Wood added 14 points and 16 rebounds for last-place Virginia Tech, which lost its eighth straight and 14th in 18 games and needed a wild rally in the final 10 seconds just to force overtime.
Eddie's 3 with 9.2 seconds left pulled the Hokies to 77-75. After Wood hit 1 of 2 free throws to give N.C. State a three-point lead, Brown fouled Green with 5.2 seconds left.
Green hit the first free throw and intentionally missed the second, and Eddie swooped in with a stickback that tied it at 78 with 4.1 seconds left.
Brown's rushed 3 at the buzzer hit off the back iron, sending the Hokies to their fourth overtime game this season and third in ACC play.
Green, who leads the nation with a 25-point scoring average, was 11 of 24 from the field while hitting the 20-point mark for the 23rd time in 25 games.
His highlight-reel jumper put the Hokies up 60-53 with just under 8 minutes left in regulation. But they didn't score again until freshman Will Johnston hit a 3-pointer with 3 1/2 minutes to play while allowing the Wolfpack to reel off 14 straight points and turn that seven-point deficit into a seven-point lead.