Connette, the Blue Devils' change-of-pace quarterback, had touchdown runs of 1, 2, 3 and 4 yards, and threw a 22-yard TD to Shaq Powell.
Duke (8-2, 4-2) -- for years, one of the nation's worst programs in a power conference -- claimed its sixth straight win, and it ranks as one of the most significant in school history.
"I remember when I first got here, the team hadn't won a game in, like, three years," running back Josh Snead said. Coach David Cutcliffe told him: "`Just believe. Believe in the process.' We got a lot of guys that believe in this process, and we're here today."
Snead rushed for a career-high 138 yards and Powell added a backbreaking 33-yard touchdown run that put the Blue Devils in complete command.
Dallas Crawford rushed for 115 yards and Stephen Morris threw for 379 and two touchdowns but the Hurricanes (7-3, 3-3) lost their third straight since climbing to No. 7. They've allowed at least 41 points in each loss.
"There's enough blame to go around in this game," coach Al Golden said.
In a wild one that featured 1,108 total yards and three lead changes, Duke -- the only two-loss team in the Coastal -- kept hold of the inside track to a berth opposite No. 2 Florida State in the ACC championship game in three weeks in Charlotte. The Seminoles have already locked up the Atlantic Division title.
Ross Martin gave Duke the lead for good late in the third quarter when he banked in a 48-yard field goal off the upright late to make it 31-30.
Two possessions later -- and two plays after Snead burst 56 yards into the Miami red zone -- Connette powered in from 4 yards out to put the Blue Devils up 38-30 with 11:37 left.
Powell then effectively iced the win on Duke's next possession when his 33-yard touchdown run on fourth-and-1 gave the Blue Devils a 45-30 lead with 6:50 left.
After Miami turned the ball over on downs, Martin added a 32-yard field goal with 1:04 left.
Morris finished 30 of 49 with touchdowns of 50 and 5 yards to Herb Waters. Stacy Coley returned a punt 79 yards for a touchdown and Matt Goudis added three field goals.
But the Hurricanes couldn't stop Duke's ground game: The Blue Devils rolled up 358 yards rushing -- by far, the most by a Cutcliffe-coached team at either Duke or Mississippi -- against a Miami run defense that gives up an average of 152.
"Coach said we were going to call it and haul it," Snead said, "and that's what we did."
Connette, who often spells starter Anthony Boone in short-yardage situations, became the first Duke player to rush for four touchdowns since Justin Boyle did it against Vanderbilt in 2006.
"People look at this game and say, `Well, Duke didn't throw the ball against Miami, but they ran it," Connette said. "No. We ran it so well, we didn't need to throw it."
Boone -- who improved to 8-0 as a starter -- was 11 of 15 for 104 yards for Duke, which continued its remarkable turnaround from perennial punchline to serious Coastal contender.
The Blue Devils went winless four times from 1996-2007 with two more one-win seasons in that span.
"It doesn't really matter to us who believes in us," Connette said. "We believe in what we're doing and we believe in the process and everything that's going on. As long as we believe in what we're doing, we're going to be a good football team."
They've already locked up their first winning season since 1994 and now they've beaten two Top 25 teams in the same year for the first time since 1971. Duke knocked off then-No. 16 Virginia Tech on Oct. 26.
The Blue Devils allowed the Hurricanes to score 10 quick points in a 54-second span of the first quarter, then fell behind 17-7 on Morris' short TD to Waters late in the first quarter.
But they outscored Miami 41-13 after Deondre Singleton's momentum-changing interception off a deflection early in the second.
Connette accounted for touchdowns on three of the four possessions after that.
"We started well. We just aren't doing a good enough job of answering on defense," Golden said. "When you get into this kind of game, you really need to be perfect on offense. We weren't. They were."