Marreese Speights added 12 points, and Thaddeus Young had 10 to help the Sixers improve to 11-14 overall and 2-0 under interim coach Tony DiLeo. DiLeo replaced the fired Maurice Cheeks on Saturday.
Luke Ridnour and Charlie Bell scored 14 points each for Milwaukee, and Mbah a Moute added 13. The loss ended the Bucks' two-game winning streak.
Brand had four points and six rebounds before he was injured. He entered the game averaging a team-best 16.4 points.
Brand signed a five-year, $80 million contract on July 9 after seven seasons with the Chicago Bulls and two with the Los Angeles Clippers. He was limited to only eight games last season with the Clippers because of a left Achilles' injury.
Bell's 3-pointer with 1:17 remaining in the third gave the Bucks a 73-63 advantage, their largest of the game.
The Sixers used a 21-7 run to take an 84-80 lead on a basket by Reggie Evans with 5:01 left.
Milwaukee missed its first eight field goal attempts in the fourth but hit seven of eight free throws.
After the Bucks eventually tied it at 86, Williams scored six straight points to give the Sixers a 92-86 lead with 1:13 remaining.
Notes: Mbah a Moute hit a 17-foot jumper at the buzzer to give the Bucks a 53-46 lead at halftime. ... Milwaukee shot 22-of-41 - 54 percent - from the field in the first half.