Harris finished 18-for-28 for 185 yards with two interceptions to help the Hurricanes rally from a 10-point deficit, outscore the Blue Devils 35-14 in the second half and outduel childhood friend Thaddeus Lewis.
The Duke quarterback - a Miami native who once taught Harris how to play the position - was 12 of 28 for 130 yards with two touchdown passes and also ran for a score, but fell to 0-3 as a starter against his hometown team.
Miami (4-3, 1-2 Atlantic Coast Conference) rolled up 420 yards in claiming its 78th straight win when scoring at least 42 points - a string that dates back to the "Hail Flutie" loss to Boston College in 1984 - but for much of the way, this one was anything but a rout.
Duke (3-3, 1-2) took a 24-14 lead early in the third quarter before Harris took over, capping a three-play, 69-yard drive with a 15-yard keeper that pulled them within three.
Harris threw a 25-yard touchdown to Travis Benjamin on Miami's next possession, then added a 10-yard TD toss to Laron Byrd in the fourth quarter to put the game out of reach.
Earlier, he had a 9-yard touchdown toss to Chris Zellner with 11 seconds left in the first half.
One of his few mistakes helped Duke match its largest lead - two plays after Adrian Aye-Darko's second interception of the game, Lewis threw a 10-yard touchdown pass to Raphael Chestnut to push the Blue Devils' lead to 10 - but it was all Harris and the Hurricanes after that.
Lewis, whose previous two losses to Miami came by an average of 7 1/2 points, also threw a 2-yard touchdown pass to Clifford Harris and ran 1 yard on a bootleg for a TD for the Blue Devils. Backup Zack Asack ran 2 yards for a touchdown with 12 seconds left for Duke.
Marve, who made his sixth straight start, was 4-for-7 for 64 yards with a 17-yard touchdown pass to Davon Johnson in just over one quarter of work. He was pulled early in the second after Aye-Darko intercepted his poorly thrown deep ball.
The Blue Devils hoped to draw inspiration from their pregame walk to the stadium that took them through Cameron Indoor Stadium, where the basketball team held its annual Blue-White scrimmage and where Hall of Fame coach Mike Krzyzewski shook each players' hand.