Hauschka made three field goals in the final quarter as the Wolfpack (4-5, 2-3 Atlantic Coast Conference) overcame a 13-7 deficit to win their third straight game -- and give coach Tom O'Brien his first-ever win at the Orange Bowl.
Daniel Evans was 19-for-40 passing for 207 yards for N.C. State, which also got a 27-carry, 89-yard effort from Jamelle Eugene.
Miami kicker Daren Daly missed two field goals, including a 27-yarder on the first possession of overtime.
The Hurricanes (5-4, 2-3) lost despite running 60 times for 314 yards against the ACC's worst run defense. But the Hurricanes simply couldn't pass the ball at all -- Kirby Freeman, playing for the injured Kyle Wright, was 1-for-14 for 84 yards and three interceptions.
Freeman's lone completion was a touchdown pass to Darnell Jenkins that put Miami up 10-0, but the Hurricanes sputtered the rest of the way.
Down 16-13 after Hauschka's 47-yarder with 6:55 left, the Hurricanes ran on the first 15 plays of their final drive of regulation, getting to the N.C. State 10 with 33 seconds left.
Out of timeouts, Miami called two passing plays, but Freeman's attempts toward Sam Shields were both broken up in the end zone.
So Daly kicked a 27-yard field goal with 19 seconds left, sending the game to overtime.
Miami got the ball first, and all six plays were rushes -- including on third-and-10 from the 12. Daly then missed a 27-yarder wide left, and moments later, the Wolfpack were celebrating.
Miguel Scott, DaJuan Morgan and Jeremy Gray had interceptions for N.C. State, which hadn't been to the Orange Bowl since 1982.
So this win was a long time coming.
Javarris James ran for 103 yards and Miami outgained N.C. State 398-317, but things were so bad offensively that, at times, the Hurricanes decided it was better to go without a quarterback.
During the second quarter, one possession after Freeman threw an interception to Scott -- receiver Lance Leggett either ran the wrong route or one Freeman wasn't expecting -- the Hurricanes had Jenkins line up as quarterback and take snaps on two straight plays.
Those two plays went for minus-12 yards, so that experiment ended quickly.
But Freeman had one great moment, finding Jenkins later in the quarter for an 84-yard TD pass.
The Wolfpack bit when Freeman faked a handoff to Graig Cooper, giving Jenkins time to get behind two defenders. He caught the ball and raced the final 40 yards to the end zone.
N.C. State became the first visitor to get a first-half score at the Orange Bowl this season with 2:04 left until intermission. Evans' 1-yard run cut it to 10-7 and capped a nine-play, 66-yard drive.
Miami went up 13-7 late in the third on Daly's 33-yard field goal -- one play after Jenkins was ruled out-of-bounds on what would have been a touchdown catch. The Wolfpack scored on their first three possessions of the fourth, with Hauschka connecting on field goals of 31 and 35 yards before his 47-yarder made it 16-13.