Harden, the 2017-18 MVP, reached the game-high double digits at Toyota Centre but was overshadowed by his rival's double-double as Antetokounmpo finished with 27 points, 21 rebounds and five assists.
The close match-up saw the Rockets lead by six points at half-time but the Bucks made the most of a powerful third quarter, outscoring their opponents 38-23, to take control of the game.
A Harden rally in the fourth got the Rockets within three points but the point guard paid the price with four missed shots and the Bucks went on to wrap up their seventh win in eight games.
Meanwhile, the Chicago Bulls suffered their fifth loss in a row as the Portland Trail Blazers used a late surge to emerge 124-112 winners.
CJ McCollum scored 24 points as Damian Lillard reached his fifth double-double of the season with 16 points and 10 assists.
In Utah, Donovan Mitchell claimed 33 points and seven assists to push the Jazz to a 106-93 victory over the Orlando Magic and help his side record their third-straight win.
It was a good night also for the Los Angeles Lakers as Kyle Kuzma sank a career-high 41 points against the Detroit Pistons.
Still without injured LeBron James, the Lakers improved to 3-5 as Kuzma used a huge third quarter to hit four three-pointers and push his team to a 113-100 win.
In-form Luka Doncic recorded 30 points as the Dallas Mavericks overcame the Phoenix Suns 104-94, while in Memphis, the Grizzlies stopped a six-game losing streak thanks to 26 points from Marc Gasol in their 96-86 win over the San Antonio Spurs.
Seven Cleveland Cavaliers players reached double figures but the were still outplayed by the New Orleans Pelicans, who triumphed 140-124, and the Boston Celtics downed the Indiana Pacers 135-108 at TD Garden.
Elsewhere, the Washington Wizards ended the Philadelphia 76ers' winning ways with a 123-106 victory and the Brooklyn Nets rallied from a 19-point deficit to beat the Atlanta Hawks 116-100.