The reigning champions were without Antetokounmpo for the fourth straight game after he entered the NBA's health and safety protocols last week.
The Bucks had lost their last two without their Greek star but Holiday finished with 24 points, 10 assists and four rebounds, while Middleton added 23 points and six assists on his return from a knee injury.
The win improves the Bucks to a 20-13 record and third spot in the Eastern Conference.
Brown shines for Celtics
Jaylen Brown scored 16 first-quarter points to finish with 34 for the game including five three-pointers as the Boston Celtics got past the Cleveland Cavaliers 111-101. Darius Garland had 28 points and six assists for the Cavs.
Paul George recorded five steals along with 17 points and six assists as the Los Angeles Clippers finished strong to beat the Sacramento Kings 105-89.
The depleted Atlanta Hawks went down 104-98 to the Orlando Magic, despite Cam Reddish's season-high 34 points.
Jokic silenced by the Thunder
Reigning MVP Nikola Jokic had a rare quiet night with only 13 points, seven rebounds and three assists as well as three turnovers as the Denver Nuggets went down 108-94 to the Oklahoma City Thunder. Shai Gilgeous-Alexander (27 points, 11 rebounds, 12 assists) had a second career triple-double for OKC.