Scott, a highly regarded recruit from New York City, scored a season-high 20 points and saved his best for last.
"Coming down the stretch, I became more confident," he said. "These are the types of games I love to play, when we've got the momentum and the adrenaline is running."
The Hurricanes (8-0) won for the first time in four games in the Big Ten/ACC Challenge. They've started a season with eight wins in a row four other times, most recently two years ago.
Minnesota (4-3) committed turnovers on three consecutive possessions in the final 2 minutes and missed 3 of 4 free throws down the stretch.
"We sort of panicked there at the end," coach Tubby Smith said. "They made plays down the stretch, and we didn't."
The Gophers have lost three games in a row by a total of 11 points. They've been plagued by disciplinary issues, and suspended freshman Royce White pleaded guilty Wednesday to a reduced charge of disorderly conduct and theft for an October shoplifting incident and scuffle with a mall guard.
"Each loss went the same way -- that's the disappointing part of it," Smith said. "There are a lot of things we need to evaluate."
While Minnesota faded at the finish, Scott shot 9-for-17 and had five rebounds, four steals and three assists in 28 minutes.
"Durand does whatever he needs to do to help his team win," Miami coach Frank Haith said. "He scored points tonight. There have been games he'll get 10 rebounds, and games where he'll have 10 assists."
Another Miami newcomer, transfer Malcolm Grant, made four 3-pointers and scored 16 points off the bench.
"This is what you live for -- to play in big games like this," Grant said. "You work hard in the summer, and this is where it pays off."
James Dews scored 11 points for the young Hurricanes, who won their 15th consecutive non-conference regular-season game. Dwayne Collins had nine points and 11 rebounds.
"We're still growing," Haith said. "We're going to make some mistakes, but we're moving forward."
Lawrence Westbrook, back in the opening lineup after missing a start for disciplinary reasons, led the Gophers with 14 points. Their starting front line totaled only 11 points and shot 5-for-17.
The Gophers finished only 7-for-15 from the free throw line.
"We've got a lot of opportunities left," Westbrook said. "We've got to have short memories."
The lead changed hands five times in the second half before Collins scored with 1:54 left to put Miami ahead for good at 55-53. Then came a flurry of Minnesota mistakes, and Scott took advantage.
"We didn't execute as a team at the end," Gophers guard Al Nolen said. "They got some steals and easy baskets, and that's what turned the game."
Adrian Thomas then forced a turnover, and Scott sank a runner for a four-point lead. Dews stripped Westbrook to force another turnover, and Scott took a long pass and dunked.
Then came another Minnesota turnover and a breakaway layup by Scott for a 61-53 lead with 29 seconds left to seal the win.
"He really attacked the basket," Smith said. "He took over the game. He was a difference-maker."
The Hurricanes shot 1-for-11 and committed seven turnovers during an 111/2-minute stretch in the first half, allowing Minnesota to turn a 17-10 deficit into a 27-21 lead.