Milwaukee's Andrew Bogut had 14 points and 17 rebounds. Rookie Luc Richard Mbah a Moute added eight points and 13 rebounds - including 10 in the first quarter - for the Bucks, who broke a three-game losing streak.
And despite being so short-handed, the Knicks still didn't play Stephon Marbury - which Knicks coach Mike D'Antoni said after the game was Marbury's decision.
Marbury was in uniform, but remained relegated to the bench - just as he has been all season. D'Antoni said he told Marbury before the game there would be minutes available if he wanted them, but Marbury declined.
Bucks fans sarcastically chanted Marbury's name with 7:25 left in the game and Milwaukee leading 88-65, then continued the chant in the closing minutes of the game.
It was the latest in a chaotic day for the Knicks, who traded Crawford to Golden State for forward Al Harrington, then sent Randolph and Collins to the Los Angeles Clippers for guard Cuttino Mobley and forward Tim Thomas.
New York's new additions might not be available to play until Tuesday's game against Cleveland, leaving them considerably short-handed for the time being.
The Knicks' leftover players kept it close until halftime, but the Bucks ultimately were able to wear them out with a pair of second-half scoring spurts.
Milwaukee led by three at halftime, then built a 57-47 lead with a 7-0 run as New York missed six straight shots to open the third quarter. Richard Jefferson opened the second half with a 3-pointer, and Charlie Bell hit back-to-back baskets for the Bucks.
The Bucks then closed the third quarter with a 7-2 run, including an inside score by Bogut, an easy layup by Ramon Sessions off a pass by Bogut and a 3-pointer by backup guard Tyronn Lue.
Milwaukee went on to score the first nine points of the fourth quarter, taking an 81-60 lead on Lue's jumper. The Knicks were shut out in the fourth quarter until David Lee hit a layup at the 9:08 mark.
Villanueva entered the game in the first quarter, his first game back after missing four games with a strained left hamstring.
