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.
At Toronto, Brunson hit 7-of-9 shots from the floor and 4-of-6 three-pointers in the first quarter to ignite an early New York surge.
The Knicks opened the second quarter with a 19-4 run to seize a 54-43 lead and stretched it to 69-52 at halftime.
Toronto, led by Brandon Ingram's 31 points, suffered a sixth defeat in seven games and a 10th consecutive loss to New York.
Wednesday's quarterfinals see Phoenix at Oklahoma City and the San Antonio Spurs at the Los Angeles Lakers.
Reigning NBA champions Oklahoma City will try to stretch their win streak to a club-record 16 games and overall record to 24-1, matching Golden State in 2015 for the best 25-game start in NBA history.
San Antonio will be without Victor Wembanyama because of a left calf strain that has sidelined him for almost a month.
