For all the great quarterbacks who have graced the University of Miami during five national championships and beyond, there is one, as of Saturday, who stands alone with the best single-game performance in school history.

Stephen Morris threw for a school-record 566 yards and five touchdowns — including the game-winning 62-yard touchdown to Phillip Dorsett with 19 seconds left — to lead the Hurricanes to a 44-37 victory over North Carolina State.

The 566 passing yards also set an Atlantic Coast Conference record.

“I saw the guy coming to hit me, and I was just trying to get it out real quick,” Morris said of the winning pass, which he threw from the UM 31-yard line and was caught near the 7 by Dorsett — 62 yards of streaking ball, with a crowd of 38,510 on its feet and ready to erupt at Sun Life Stadium. “People dream about it, but it’s kind of crazy when you’re actually in the moment. I’m speechless about it. I don’t know what to say. I don’t know how many more I have in me.”

Dorsett caught seven passes for 191 yards and two touchdowns — UM’s sixth all-time receiving performance for a single game. Fellow receiver Rashawn Scott added 180 yards and two touchdowns on six receptions — tied for No.10 in single-game receiving yards.

Their performances came on the heels of a 42-36 overtime victory at Georgia Tech last week.

But as stellar as the UM offense performed, the defense had issues. The Wolfpack’s 664 yards were the second most ever allowed by a Hurricanes team, including a career-high 440 yards and four touchdowns for N.C. State quarterback Mike Glennon.

The good part: UM forced six turnovers, the fifth of which — cornerback Thomas Finnie’s interception at the UM 39-yard line with less than a minute left in the game — led to Miami’s winning touchdown.

“It doesn’t matter the amount of yards we gave up, a win’s a win,” Finnie said. “We outplayed their defense. We kept playing and didn’t give up and still won.”

The Hurricanes (4-1) are 3-0 in league play for the first time since 2004, their inaugural year in the ACC. UM, which produced 651 yards of offense — third all-time in school history — will face 10th-ranked Notre Dame (4-0) next Saturday night at Soldier Field in Chicago. Morris played against the Irish in a losing effort on New Year’s Eve 2010 in the Sun Bowl.

“I talked about it when we were huddling up as a team in the locker room,” Morris said when asked about Notre Dame. “They had a bye week, so we have to do a great job of making sure we stay fresh. And we’ve got to make sure that we have good leaders [Saturday night] and make sure no players are doing anything out of control.

“But I’ve been waiting for this game since freshman year. It’s going to mean a lot to me and my family. It’s going to mean a lot for this program. So, we’re going to really make sure that we’re ready for this game. We’re going to really make sure that we study and try to play our best game.”

Morris’ 566 yards (he completed 26 of 49 passes and also threw an interception) surpassed former Heisman Trophy winner Gino Torretta’s 485 yards against San Diego State in 1991 — one of UM’s national-title years.