Jabari Parker added 17 points, including a dunk and a jumper during the decisive spurt that pushed Milwaukee to a double-digit lead.
The Knicks trailed by 21 with 7:04 left in the third quarter when coach Derek Fisher replaced his entire starting five following a technical foul on Jose Calderon at the end of the run. Frustrated starters argued with the officials.
The fresh lineup settled the team, though New York could get no closer than nine the rest of the night.
Carmelo Anthony scored 18 points for the Knicks.
Normally a shooting guard, O.J. Mayo started at point guard with Milwaukee minus three injured ball-handlers. Mayo scored 17 points.
But Carter-Williams, the Bucks' only heathy true point guard, played well off the bench. The third-year guard had lost his starting job because of inconsistency.
The Bucks took relatively good care of the ball despite the adversity at the point, while the big guys gave Milwaukee a lift up front.
Greg Monroe had 18 points and 14 rebounds, and beat the Knicks with his mid-range game. Parker, who is returning from a left knee injury, showed spurts of athleticism and a tough-to-stop baseline move while playing a season-high 36 minutes.
Rookie Kristaps Porzingis had 12 points for the Knicks. He drew sneers after slipping to the floor while fouling Johnny O'Bryant on a drive, and then impressed the crowd later in the second quarter by swooping by three defenders around the bucket for an athletic putback off a rebound.
Knicks: Fisher said G Aaron Afflalo is getting more comfortable after missing the preseason with a hamstring injury. Afflalo, who missed the season's first eight games, is averaging 13.6 points.
Bucks: PG Jerryd Bayless was using crutches and wearing a boot on his left foot before the game. He hurt his ankle during Friday night's loss at Detroit. … PG Greivis Vasquez missed his fifth game because of right ankle soreness. Kidd said he hopes Vasquez can start running in the next few days. … PG Tyler Ennis sat out with left shoulder soreness.