The Eagles (3-7) are suffering through their worst season since going 4-7 in 1998 under Tom O'Brien — now in his fifth season as head coach at North Carolina State.
Rettig completed 9 of 13 attempts for 118 yards, and Andre Williams carried 18 times for 61 yards.
Mike Glennon completed 28 of 40 passes for 220 yards and James Washington had a 3-yard TD run for the Wolfpack (5-5), who moved deep into BC's territory in the closing minutes before Glennon's pass was tipped at the line and fell to the ground on a fourth-and-5 play with 1:10 left.
NC State needs to win both of its final games to become bowl eligible because it has two wins over FCS schools. The Wolfpack hosts No. 9 Clemson and Maryland to close the season.
Wolfpack corner back David Amerson extended a school-record with his NCAA-leading 10th interception in the first half. NC State held BC to minus-2 yards of total offense in the second half.
Boston College linebacker Luke Kuechly had 18 tackles — nine in the final 13 minutes — for his 32nd straight game with double digits in tackles. He entered the game leading the nation with 150 after leading the nation with 183 last year.
The Eagles led 14-3 at halftime.
North Carolina State started at its own 18 with 13 1/2 minutes left in the game and marched down to the Eagles' 23 before Donnie Fletcher picked off Glennon's pass in the end zone.
Boston College took the opening kickoff and marched right down the field in five plays, grabbing a 7-0 lead when backup quarterback Bordner scored on a 3-yard run off an option play. The score came two plays after Rettig hit Alex Amidon with a 41-yard pass along the left sideline, moving the ball to the Wolfpack's 9.
NC State, coming off a shutout win over rival North Carolina last week, drove 61 yards in 13 plays on its first possession before the drive stalled and Niklas Sade kicked a 32-yard field goal. Glennon completed 7 of 8 passes for 60 yards with the only incompletion a drop by T.J. Graham.
The Wolfpack had four first downs on their first drive of the game, but only had three more until midway into the final quarter.
The Eagles improved their lead to 14-3 late in the first half on Rettig's 17-yard TD pass to Colin Larmond Jr. BC started with good field position after Wil Baumann's 24-yard punt gave them the ball at their own 41. Rettig completed consecutive passes for a combined 23 yards and Williams carried six times — mostly up the middle — for 16 yards.
Except for the final possession — which was a one-play kneel down to end the half — BC went into NC State territory each time it had the ball in the first half.
Washington's scoring run cut it to 14-10 midway into the third quarter. On a third-and-4 from the Eagles' 38, Glennon lofted a pass to tight end Quinton Payton that dropped in between four defenders.
Late in the first half, a fan wearing a No. 40 BC jersey ran onto the field from the student section toward the line of scrimmage. Wolfpack offensive tackle Rob Crisp knocked the male intruder to the ground with his right arm before he got up and was taken off the field by security.