Richard Jefferson added 21 points for the Bucks, who snapped a season-long four-game skid. Luke Ridnour chipped in 12 points and 10 assists in the win. Dan Gadzuric logged 11 points and 14 boards.
Jefferson, Luc Mbah a Moute and Villanueva all drained buckets to open the fourth quarter to give the Bucks an 82-72 lead with 9:15 left.
Rose interjected with a three-point play, but Villanueva rattled off seven straight points to make it 89-75 just prior to the midway point of the fourth.
"We fought our way back but if there was a big play or a big basket it wasn't from us," said Deng.
Rose's two free throws capped an 11-2 Bulls run that brought the visitors within 93-88 with 1:56 showing on the clock, but the Bulls were unable to get any closer than five points down the stretch.
The Bulls led 20-19 after the first quarter but fell behind, 54-42, at the intermission.
Down by 15 midway through the third stanza, the Bulls used a 14-2 run to get back into the contest. Deng's three-pointer sparked the run and Gordon scored the rest of the points to make it 71-68 with just under two minutes left in the frame.
"Obviously we had a very good first half," Bucks head coach Scott Skiles said. "We came out in the third and we were a little flat again, especially on the defensive end."
Chicago trailed 76-72 heading into the final 12 minutes.