The Greek two-time NBA Most Valuable Player had been expected to immediately propel Miami into the ranks of Eastern Conference contenders, but his first victory in a Heat uniform came at the fifth attempt.
Antetokounmpo, who had a triple-double in defeat to the Dallas Mavericks two nights earlier, again racked up impressive numbers, with 24 points and 18 rebounds.
This time he was backed up by teammates Bam Adebayo, who scored 24 with nine rebounds, and Andrew Wiggins, who added 18 points.
Former Milwaukee Bucks star Antetokounmpo reached 1,000 career steals while Adebayo became the Heat's all-time leading rebounder, surpassing the record of 5,791 previously held by Udonis Haslem.
The star-packed Philadelphia 76ers bounced back from Sunday's disappointing loss against Detroit to move to 4-1 with a 114-109 victory in a back-and-forth clash with the Indiana Pacers.
The new home of LeBron James struggled to see off Indiana, which this week announced it would be without star Tyrese Haliburton for around two weeks due to a hamstring injury.
The Sixers fell behind in a lopsided third quarter, but rallied down the final stretch to seal a road victory.
Tyrese Maxey scored 17 of his 27 points in a blistering fourth quarter showing to spare his team's blushes.
James managed just 13 points but added 10 assists, while Joel Embiid had 21 points and 11 rebounds, and Jaylen Brown provided 20 points.
AJ Dybantsa, the top overall pick of the recent NBA Draft, played his first NBA minutes during the Washington Wizards' 121-111 loss to the Cleveland Cavaliers.
Nineteen-year-old Dybantsa had missed the Wizards' first four games with an ankle sprain but started Wednesday, scoring 19 points.
The Cavaliers clinched victory in the final quarter. Donovan Mitchell scored 19 points with seven assists.
Follow the NBA better than ever
The best basketball league in the world is back, and Flashscore is improving our coverage of the NBA with match previews based on key stats and facts ahead of each game!