Morris was 26-of-50 passing for Miami, which finished with 652 yards of offense and survived despite wasting a 10-point lead in the fourth quarter.
Mike Glennon completed 24 of 42 passes for 441 yards and four touchdowns for N.C. State (3-2, 0-1), but his interception with 48 seconds left set up Miami's winning score.
Three plays later, Morris scrambled, bought some time and found Dorsett for the game-winner.
The Hurricanes led 37-27 with 8 minutes left before the Wolfpack rallied. Glennon's 6-yard pass to Rashard Smith got N.C. State within 37-34. And with 1:58 left, Niklas Sade - who missed an extra point earlier - connected on a 50-yard field goal, tying the game.
Morris started the ensuing Miami drive with an 18-yard pass to Scott, a completion that gave him 487 yards on the day, two more than Gino Torretta's previous mark of 485. The drive stalled not long afterward, and Miami punted it away with 1:03 left.
N.C. State kept the ball for 15 seconds before giving it back, and Miami - which hadn't cashed in turnovers all day - finally came through on the Morris-to-Dorsett pass.
Tony Creecy rushed for 120 yards on 19 carries for N.C. State, which turned the ball over six times, including one on the game's final play.
It was wild, back-and-forth football throughout, and the fireworks started early.
Miami scored 23 points in a span of 4 minutes, 12 seconds in the first quarter - its second straight game with a 23-0 run, matching the way it ended last week's overtime win at Georgia Tech. Morris connected with Scott on a 52-yard pass to set up Miami's first touchdown, a 13-yard throw to Allen Hurns, who made a spectacular tiptoe catch at the side of the end zone to knot the game at 7-all.
The Hurricanes got a safety on their next possession, their second in as many games, and things started rolling. Morris and Hurns hooked up for 40 yards on the ensuing drive, capped by Morris finding Dorsett for a 24-yard touchdown. After a three-and-out by the Wolfpack, Morris and Scott connected again, this time on a 76-yard scoring play.
Just like that, Miami was up 23-7 with 4:18 left in the first quarter.
And that was when the Wolfpack started to self-destruct. Miami, however, simply wouldn't let them do so.
N.C. State fumbled the ball away on four of its next five possessions - and the Hurricanes got exactly zero points off those gifts. Miami gave the first of those turnovers back after a pass skipped off tight end Clive Walford's hands for an interception in the end zone, a play where the Hurricanes could have taken a 30-7 first-quarter lead.
On its next three fumble recoveries, Miami responded with an interception, a punt and a missed field goal by Jake Wieclaw, a 19-yard chip shot that caromed off the left upright. That miss came after the Hurricanes had gone for a fake field goal on fourth-and-2 from the N.C. State 8, with holder Dalton Botts keeping the ball and breaking tackles for a first down, a play that was ultimately wasted.
Wieclaw missed three field goals on the day, but the Hurricanes survived anyway.