New York's Quentin Richardson scored 22 points and Zach Randolph and Jamal Crawford each added 19.
The Knicks lost their fifth straight road game and are 2-15 in their last 17 games.
Simmons, who averages 6.7 points per game, scored the first six points in overtime to give Milwaukee a 115-111 lead with 2:45 remaining.
After a basket by Wilson Chandler cut Milwaukee's lead to 115-113, Desmond Mason hit a shot and Bogut added a free throw for a 118-113 lead with 1:11 remaining.
Crawford then threw a pass out of bounds, but Simmons was called for an offensive foul on the other end.
On New York's next possession, Randolph missed a jumper and Richardson missed a 3-pointer.
Redd made a free throw with 16.7 seconds remaining and Richardson's field goal put the score at 119-115 with 4.7 seconds left.
New York forced overtime when Richardson made two of three free throws with a second left.
After Simmons' lay-up gave Milwaukee a 109-107 lead with 1.8 seconds remaining, Richardson was fouled by Ramon Sessions on a 3-pointer from the corner.
Richardson's first free throw bounced off the front rim but he made the next two to tie the score at 109-109. Milwaukee was unable to get a shot off before the buzzer.
New York started the fourth quarter with an 88-77 lead but Milwaukee used a trapping press and scored the first 11 points to tie the score at 88 with 8:30 remaining.
