Raina Perez stole the ball at midcourt and made a layup with 14 seconds left to lift NC State to a 66-63 win over Notre Dame.
It is the first trip to the Elite Eight for the Wolfpack since 1998, when they reached the Final Four.
The Wolfpack scored 15 of their final 19 points in the fourth quarter, capped by Perez's layup. The Irish had one last chance, but Westbeld missed a 3-pointer from the wing and Perez hit both free throws for the final margin.
Perez said he knew he could do it, and he knocked them down.
Cunane made the first of her two free throws with 36 seconds left to help the Wolfpack get within 63-62. After a Notre Dame timeout, the Irish got the ball in the backcourt and Perez took it in for a layup and the lead.
NC State will face either Connecticut or Indiana in the regional final.
The Wolfpack avenged an earlier loss to the Irish by getting 16 points from Cunane and 14 from Kai Crutchfield. NC State lost its most recent game on Feb. 1
It was a hump we had to get over, and the girls are determined and I am determined and we made it happen.
Westbeld added 13 to his 21 points for the Irish.
The Notre Dame basketball team is back among the nation's elite after two years under coach Niele Ivey. The Irish missed out on the NCAAs last year.
The Irish got going behind freshman Miles after the Wolfpack led 16-12 at the end of the first quarter. The Irish scored seven straight to open up a 36-26 lead. The Wolfpack was behind at the half. The lead was around eight for most of the third quarter.
There is a big picture.
The Irish are a young team that is going to be one of the top teams in the country.
NC State struggled most of the game, but found a way to win in the end and reach the Elite Eight with a senior-led squad.
How did they get here?
The Irish beat UMass in the first round and then beat Oklahoma in the second.
NC State defeated both Kansas State and Longwood to advance to the Sweet 16.