N.C. State never trailed and shot 50 percent but allowed nearly all of an 18-point lead to slip away.
Warren hit a free throw with 5.9 seconds left. Detroit got a good look on its final possession but Jarod Williams' deep 3 bounced off the iron as the buzzer sounded.
Warren has led or shared the scoring lead in every game but one for N.C. State, which improved to 13-0 in the school's annual heritage games at its former home — on-campus Reynolds Coliseum.
And it looked like Turner had put N.C. State in complete control after he scored on three consecutive trips down court to give the Wolfpack their largest lead.
He hit two 3s before a jumper with just under 8 minutes left made it 65-47.
But the Titans wouldn't go away.
Howard scored eight points in the final five minutes, hitting a big 3 with 4½ minutes left before his drive with 3 minutes remaining pulled Detroit within single digits at 72-64.
His uncontested 3 from the top of the key with just under 2 minutes to play cut the lead to 74-69.
Bruinsma's layup with 48.7 seconds remaining made it 77-73, and his 3 with 29.1 seconds left pulled the Titans to 79-76.
Turner's free throw with 27.7 seconds remaining made it a four-point game. After Detroit's Carlton Brundidge was called for walking with 19.4 seconds left, Desmond Lee hit a free throw to make it 81-76 before Grant's big 3 made things even tenser.