Antetokounmpo scored 37 points with seven rebounds and four blocked shots for the Bucks, who reached the semi-finals of the in-season tournament for the second year in a row and will face either the New York Knicks or Atlanta Hawks for a place in the final.
Damian Lillard scored 15 of his 28 points in the fourth quarter and handed out nine assists for the Bucks, who had all they could handle from Orlando despite the absence of injured Magic stars Paolo Banchero and Franz Wagner.
Lillard threw down a dunk to put the Bucks up 108-107 with 32.6 seconds remaining, and after Orlando's Jalen Suggs missed a three-pointer, Lillard drilled a pair of free-throws to push the Bucks' lead to three points with 9.1 seconds left.
Antetokounmpo and Lillard each added a pair of free throws in the final seconds to seal the hard-fought victory.
"We fought for this one," said Lillard, who said the Bucks would be aiming to improve on their performance last year in the inaugural edition of the event when they head to Las Vegas for the final stage.
"We didn't have the greatest experience there last year," he said. "So I think all of us are thinking (about) going back and finishing what we started last year and doing it right this time."
Suggs scored a career-high 32 points and pulled down nine rebounds for the Magic, who got off to an aggressive start on the way to a 33-25 lead after one quarter.
Suggs had three of the Magic's seven steals in the first period as Orlando kept the Bucks off-balance.
Milwaukee recovered to lead 60-59 at half time, and after four lead changes in the third quarter, the Bucks took an 80-72 lead into the final period.
They would swap the lead four more times before the Bucks finally put it away.
Thunder silence Mavs
In Oklahoma City, Shai Gilgeous-Alexander and the Thunder turned the highly anticipated matchup of two of the league's hottest teams into a rout, beating the Mavs 118-104 to end their seven-game winning streak.
Gilgeous-Alexander scored 39 points with eight rebounds and five assists. Jalen Williams added 18 points and center Isaiah Hartenstein added 10 points and 13 rebounds for the Thunder, who made 20 of their whopping 50 three-point attempts.
Oklahoma City notched their eighth win in nine games and will play either the Houston Rockets or Golden State Warriors for a place in the final.
The Thunder's top-ranked defense proved too much for the Mavs. Klay Thompson scored 19 points for Dallas, Kyrie Irving added 17 and Luka Doncic, coming off back-to-back triple-doubles, was held to two points in the first half and finished with 16 points and 11 rebounds.
Oklahoma City parlayed 19 Mavs turnovers into 36 points and won the rebounding battle 52-44.
The quarter-finals will conclude on Wednesday when the Knicks host the Hawks and the Rockets host the Warriors.
The action then shifts to Las Vegas for the semi-finals on Saturday and the final on December 17.
With Vegas beckoning, Gilgeous-Alexander said the game against a Mavs team that ousted them in last year's playoffs had "a little bit of a playoff feel, a little bit more at stake than just a regular-season game.
"I'm proud of the team, proud of the guys," he said. "We rose to the moment."
