The victory moved the Bucks within 1 1/2 games of Detroit in the Central Division.
"We played like we had been on vacation for six days and maybe we were, but that was good for us," Buck Coach Don Nelson said.
"Let's hope it starts us back on our way for a stretch drive. We'd love to make this a close race and love to go down the stretch here and start winning some ball games. The good news is that we picked up a full game.
The Clippers held a 64-63 lead late in the third quarter, but Milwaukee went on a 16-6 run to close the third quarter with a 79-70 lead.
Milwaukee led, 91-78, with 6:42 left, but the Clippers ran off seven straight points to get within 91-85 with 5:15 remaining on Darnell Valentine's three-point play. Mike Woodson, who had 23 points, hit a three-pointer with two minutes left to draw the Clippers up to 100-93.
But the Bucks put the game away on a basket by Lucas and a three-point play by Jack Sikma to lead, 105-94, with 1:15 remaining.
The Clippers made 57% of their shots but also had 27 turnovers.
"That was a winnable game," Clippers' Coach Don Chaney said. "Every game we play we have to be able to take care of the basketball. You shortchange yourself when you don't even have the opportunity to score.
"Once we got down 10 points, it's very difficult for us to come back because of the talent we have. We don't have explosive players that can put us back in games."
Rory White had 15 points and Quintin Dailey 14 for the Clippers.