The Magic, without top scorer Franz Wagner due to a high ankle sprain, won for the 11th time in 15 games and improved to 5-0 in Cup play.
Bane went 6-of-9 from three-point range, added six rebounds and five assists, and Jalen Suggs scored 20 for Orlando.
"We need these reps. We need to play in these meaningful games," Bane said. "We're a young team trying to make something happen like a run so we need these moments."
Orlando will face the winner of a later Cup quarter-final between New York and Toronto in Saturday's semi-finals at Las Vegas.
Bane scored 15 points in the fourth quarter to deny Miami any chance of a comeback.
"Winning time," Bane said. "That's all I care about is winning."
Paolo Banchero, who returned last Friday after missing 10 games with a groin strain, added 18 points for the Magic, who delivered Miami a fourth consecutive loss.
Orlando beat Miami in their two prior meetings this season, but the Heat seized a 15-0 lead with Tyler Herro scoring seven points, and held a 30-17 lead after the first quarter.
A 14-4 run in the second quarter lifted the Magic and Miami's lead was reduced to 57-56 by halftime.
Orlando were 89-83 ahead after the third quarter and opened the fourth with a 9-2 run to extend the lead to 98-85 and seize control.
Norman Powell led Miami with 21 points, Herro had 20. Bam Adebayo and Andrew Wiggins each contributed 19.