Corey Maggette hit a tiebreaking 3-pointer in the final minute of overtime and the Bucks beat Toronto 116-110, handing the Raptors their 10th straight loss.
Maggette's decisive basket bounced on the rim, leaving him anxiously watching and waiting for it to fall through.
"The man upstairs kind of tapped it down for me," Maggette said. "I'm just glad I made the shot."
Bogut figured the Bucks were due some good fortune because their most recent lucky shot was his buzzer-beating tip-in against Indiana on Dec. 8.
"We needed a lucky bounce," Bogut said. "We haven't had a lucky bounce for a number of games. Teams always get them against us so it was about time we got one back."
Maggette had 29 points and 11 rebounds, and Bogut scored six of his 24 points in overtime as the Bucks won their second straight and fourth in six games.
"Bogs and Corey carried the load offensively tonight," coach Scott Skiles said.
Ilyasova made nine of 10 field goal attempts, including two 3-pointers, and went 5 for 5 from the line.
"He was very efficient," Skiles said. "You could tell when it was coming out of his hand that he was in one of those grooves tonight."
Ilyasova also scored 25 at New York on Feb. 5, 2010.
"In my opinion, he's one of the best shooters in the world for a four-man," Bogut said.
Amir Johnson scored a season-high 24 points and added 12 rebounds, Andrea Bargnani scored 23 and Jose Calderon had 13 points and 11 assists for Toronto, which matched its longest losing streak since a 10-game slide from March 26 to April 12, 2006.
DeMar DeRozan had 11 points for the Raptors, shooting 5 for 14. Bargnani finished 9 for 23.
"It's tough, our best guys didn't have very good games tonight," Raptors coach Jay Triano said. "DeMar and Andrea struggled a little bit tonight and that's going to happen sometimes."
Before the game, Skiles said he expects guard Brandon Jennings will be able to play "very limited minutes" in Saturday night's home game against New Jersey. Milwaukee's leading scorer at 17.9 points per game, Jennings has not played since Dec. 18 because of a broken foot.
Toronto trailed 97-87 on a 3-pointer by Ilyasova with 6:31 remaining, but tied it at 104 with 18 seconds left in regulation.
The Bucks gave the ball to Delfino, who let the clock wind down before driving and losing the ball out of bounds, giving it back to Toronto with 2.8 seconds left. Bargnani's jump shot at the buzzer didn't fall, sending the game to overtime.
Bogut scored the first six points of overtime, but baskets by Johnson and DeMar DeRozan made it 110-108 with 1:35 remaining. Keyon Dooling missed a pair of free throws, allowing DeRozan to tie it with a reverse layup. Maggette answered with his tiebreaking 3, giving the Bucks a 113-110 lead with 43 seconds to play.
Sonny Weems missed a 3 at the other end and Delfino was fouled after picking up the rebound, but made just one of two. After another Toronto miss, Maggette sealed it with a pair of free throws.
Bogut started hot, making six consecutive shots before his first miss. He scored 12 points in the first as the Bucks led 32-22 after one.
Toronto's reserves turned things around with a superb second, scoring 25 of the team's 35 points in the quarter. Milwaukee took an 81-78 lead into the fourth.
Toronto has not led going into the final quarter since Jan. 12 against Atlanta, a run of nine games. The Raptors led 77-75 that night but lost 104-101 on a late 3 by Mike Bibby, the first defeat of their current losing streak.
Calderon started for Toronto despite lingering flulike symptoms that kept him out of Monday's loss to Memphis. ... Milwaukee's Drew Gooden (left foot) and John Salmons (right hip) did not make the trip to Toronto.
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