They erased an 18-point first-half deficit, rallied in the final minute to force overtime, then made the decisive stop in the extra session to win their fourth straight.
Trevor Lacey scored 13 points and Kyle Washington added 12 for N.C. State (13-8, 4-4), which has lost three of four since upsetting then-No. 2 Duke two weeks ago.
The Wolfpack had a chance to force a second OT after Demetrius Jackson's free throw with 12.4 seconds left made it a three-point game.
Grant got a hand on Lacey's 3-point attempt with about 4 seconds left. Another 3 by Lacey at the buzzer rimmed out.
Jackson finished with 11 points and Zach Auguste added 10 points and 11 rebounds for Notre Dame, which seemed destined for its first ACC loss on the road this season after the Wolfpack led by four in the final minute of regulation.
Jackson pulled the Irish to 71-69 with a layup with 18.7 seconds left, and Lacey's deep inbounds pass went out of bounds off Cody Martin with 16.5 seconds to go.
Beachem tied it by putting back Connaughton's third-chance attempt with 1.8 seconds left, and Notre Dame got the ball back when Abdul-Malik Abu was called for pushing off while catching the long inbounds pass. Grant's halfcourt shot at the buzzer bricked off the back iron.
Caleb Martin had 12 points, Ralston Turner added 11 and Cody Martin scored 10 for the Wolfpack, who sure looked headed for another top-10 upset after they went up 40-22 in the first half on the third dunk in a row by BeeJay Anya.
The Fighting Irish erased that huge deficit with a 31-12 run. They hitting five 3s in the first 6 1/2 minutes of the half -- including two in a row by Jackson -- and Auguste followed the second of those with a fast-break layup that gave Notre Dame its first lead, 53-52, with 13 1/2 minutes left.