The Bucks got to within 96-94 with 6 seconds left on a pair of baskets by Brandon Jennings.
Gerald Wallace inbounded to Williams, but Jennings was draped over his right side. The contact shook the ball loose and it appeared to hit Williams' foot before rolling out of bounds. After review, the Nets had possession. Williams was fouled and made one of two free throws to make it 97-94 with 3.4 seconds left.
Williams then fouled Ellis on a hurried 3. Ellis missed the first two shots, and intentionally missed the third.
Jennings scored 31 points and had 11 assists for Milwaukee.
C.J. Watson had 17 off the bench for Brooklyn which took both games of the home-and-home set that started with the Nets' 113-111 overtime win on Tuesday night. Joe Johnson won the game in Brooklyn with a late game-winning jumper.
It was the Nets' fourth consecutive win, all against teams currently holding a playoff spot. With the Knicks losing to Indiana 125-91, the Nets pulled to within one game of first-place New York in the Atlantic Division.
Andray Blatche scored 12 points and had 12 rebounds for the Nets
Williams, who had 19 points and nine assists Tuesday after sitting out the previous two games with inflammation in his ankles, played 33 minutes. He had eight assists and one steal.
The Nets took advantage of the Bucks' inability to hit shots in the fourth quarter with a 19-5 run.
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Williams' 3 at 1:50 gave Brooklyn its biggest lead at 94-83 lead. The Bucks held the Nets scoreless for the next 1:35.
The Nets used a 16-1 run spanning the third and fourth quarters and took the lead 77-76 on Blatche's layup with 10:11 left to play and MarShon Brooks made two free throws to push the lead to 79-76.
Ellis that stopped a Bucks' scoring drought that lasted a little less than seven minutes. He made one of two free throws with 8:11 to go, but Johnson hit a jumper to put Brooklyn up by four.
The Nets trailed 54-42 at the half, but used a 7-0 run in the third quarter to pull to 66-61 with 4:25 left. Williams made a 3 and Watson a layup before Wallace's dunk off a miss by Jennings, who was nine of 10 until Brook Lopez blocked his shot.
The Bucks were 21 of 34 (61.8 percent) the first half while the Nets struggled and made 15 of 46 shots (32.6 percent).
Jennings had 18 points before the break, making all seven of his shots, and seven assists. Ersan Ilyasova had 10 points and seven of Milwaukee's 23 rebounds.
NOTES: Larry Sanders extended his NBA lead to 19 games with four or more blocks in a game. ... Before the tip-off, there was a moment of silence in remembrance of the owner of the Los Angeles Lakers, Jerry Buss, who died Monday. ... The Nets improved to (18-8+) under interim coach P.J. Carlesimo, the second-best start under any of their previous 21 coaches. Lawrence Frank's team started 19-6 in 2003-04.
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