It was another magisterial performance from Mitchell, who scored 39 points two days after pouring in 50 in the Cavs' game six defeat.
This time he had plenty of scoring support from teammates as the Cavs erased an 18-point second-quarter deficit to clinch a series in which the home team won every game.
Caris LeVert scored 15 points off the bench and Max Strus scored 11 of his 13 points in the third quarter, when the Cavs out-scored the Magic 33-15 to take charge.
Evan Mobley scored 11 points with 16 rebounds and five blocked shots to help Cleveland withstand a 38-point performance from Paolo Banchero.
The Cavs, with starting center Jarrett Allen sidelined a third straight game with bruised ribs, moved on to the second round a year after a stinging first-round loss to the New York Knicks.
"I didn't want to go home," Mitchell said of the mindset that saw him score 17 points in the third quarter as he virtually willed Cleveland to the lead.
The Magic delivered a strong first punch, Banchero scoring 10 points in the first period as Orlando grabbed a 24-18.
In the face of Orlando's suffocating defense the Cavs connected on just six of 22 shots in the first quarter and didn't make a three-pointer until Sam Merrill drilled one midway through the second quarter.
The Magic pushed their lead to as many as 18 points in the second quarter before the Cavs clawed back to cut the lead to single digits.
Banchero's layup in the closing seconds of the first half saw Orlando take a 10-point lead into the break, but momentum was on Cleveland's side and they overwhelmed the Magic in the third.
Mitchell, relentless in the paint, tied it at 64-64 with a floater and LeVert drained a pair of free throws to give the Cavs their first lead since the first quarter.
Strus hit back-to-back three-pointers as Cleveland built a 76-68 lead going into the final period.
The Cavs pushed their advantage to 14 points in the final frame, fans chanting "We want the Celtics" as the final minutes ticked off.
It was a crushing end to a strong season for the Magic, collectively the second-youngest team in the playoffs behind the Oklahoma City Thunder.
Wendell Carter Jr. scored 13 points and Jalen Suggs added 10 for the Magic, but Franz Wagner was held to just six as Orlando remained in search of a first playoff series victory since 2010.
