The Fighting Irish (15-2, 4-0) outscored Miami 10-1 down the stretch to earn their sixth straight victory. Their four league wins have been by a total of 18 points.
"Our fan base is all on heart medication," coach Mike Brey said. "I loved our mental toughness again to finish."
A sellout crowd failed to rattle the Irish, who snapped Miami's 21-game home winning streak.
The Hurricanes (11-4, 1-2) led 61-57 with 2:30 left before Notre Dame rallied.
"Obviously we have some experience there," Irish junior Steve Vasturia said. "It's a testament guys not being afraid to step up and staying confident. We've been able to get big defensive stops in all four of these wins; that has been the backbone."
Beachem's reverse layup put the Fighting Irish ahead 63-61 with 1:04 to go. After Ja'Quan Newton made one of two free throws for Miami, Vasturia drove for a layup with 8 seconds remaining.
Following a timeout, Beachem, a New Haven High School alum, made a steal on the inbounds play, and Matt Farrell's two free throws iced the victory.
Miami coach Jim Larranaga declined to blame his young team's inexperience on the fade at the finish.
"It's more of a factor of how cool, calm and collected Notre Dame is at the end of these games," Larranaga said.
Notre Dame won despite shooting a season-low 37 percent, with Miami blocking a season-high 12 shots.
"We're really mentally tough," Brey said. "We're not affected when a guy rejects one off the backboard and the crowd goes crazy. We bounce back and keep playing."
Farrell led the Irish with 15 points and six assists, and Beachem had 13 points. Vasturia added 10 points and six assists.
Miami senior Davon Reed tied a career high with 21 points but made a critical late turnover.
"We just didn't take care of the ball late in the game," Reed said. "We didn't have poise down the stretch."
The Hurricanes had 13 turnovers to only six for Notre Dame.
The Fighting Irish outscored opponents 25-6 in the final 6:42 of their first three league games. Their other conference wins were by one, seven and five points.
"That's four games in a row where we've made plays in game situations," Brey said. "We believe that in those situations we're going to figure it out. It certainly is a little bit of a psychological advantage for us now."
Bonzie Colson went 2 for 12 against the Hurricanes and was held to a season-low eight points, less than half his average.
"Their length and athletic ability really bothered him," Brey said. "It is the first time someone has totally taken him away."
Colson had 11 rebounds.
The Irish led only briefly in the first half but outscored Miami 10-0 to begin the second half and take a 38-28 lead. Colson started the run with a 3-pointer, and Martinas Geben finished it with a dunk.
Notre Dame had its biggest lead at 50-39 before the Hurricanes went on a 13-2 run to forge a tie and set the stage for the frantic finish.
The Hurricanes wore cream 1960s-style uniforms.
Miami junior forward Michael Gilmore, a transfer from Virginia Commonwealth, was dismissed from the squad for "failure to meet team expectations." He was to become eligible next season.
Notre Dame will remain on the road to play at Virginia Tech on Saturday. That's the second of three consecutive away games for the Irish.
Miami plays at Pittsburgh on Saturday, and its next three games are on the road.
"No time to mope around," Reed said.