Brown set up his game-winning touchdown with a 16-yard run.
The N.C. State defense had recovered a fumble by East Carolina quarterback Patrick Pinkney on the third play in overtime.
Russell Wilson led the Wolfpack (2-2) with three touchdown passes to different receivers. Wilson completed 21 of 31 passes for 210 yards.
Brown rushed for 73 yards on 12 carries and tight end George Bryan scored once on five receptions for 58 yards.
Pinkney was 19 of 32 for 210 yards with one touchdown and one interception.
Dwayne Harris gained 88 yards on 10 receptions and Norman Whitley scored once on nine carries for 83 yards for the previously unbeaten Pirates (3-1).
It was the second straight year the Pirates lost to their intrastate opponent.
They failed to score on two possessions in the red zone in the fourth quarter.