John Salmons added 20 points for the Bucks, who were playing their second game without point guard Brandon Jennings, the club's top scorer who has a broken left foot.
They had lost to the Lakers six straight times and were coming off a 106-80 loss at Portland on Monday.
Ersan Ilyasova scored 17 points for Milwaukee, who seized the lead early and finished the contest with a 21-7 scoring run. A tenacious Bucks defense held the Lakers scoreless for almost four minutes late in the contest.
Australian big man Andrew Bogut scored 15 points for the Bucks, who were without not only Jennings but also Corey Maggette and Drew Gooden.
Gooden is away from the team to get treatment on his injured right foot, while Maggette missed his second straight game with an apparent concussion.
The 1.65m (5-foot-5-inch) Boykins, the improbable stand-in for Jennings, drained four three-pointers.
"Boykins was our dark horse, there," Bogut said. "He really played well for us tonight, hit big shots for us." Kobe Bryant scored 21 points and Pau Gasol added 15 points and 11 rebounds for Los Angeles, who perhaps got caught looking ahead to a Christmas showdown on Saturday against LeBron James and the Miami Heat.
"It was mentioned (by the players who said) 'don't mess around and let this game get away from us,'" Lakers coach Phil Jackson said of his team's awareness that they shouldn't overlook Milwaukee.
Nevertheless the Lakers came out flat. Coming off their big defeat in Portland, Bogut said the Bucks weren't about to get caught looking at anything but the task in hand.
"We came out and laid an absolute egg and got blown out," he said of Monday's contest. "We knew we had to come out tonight and give an effort win or lose and we did that."
In another interesting match, the Dallas Mavericks became the latest team to topple the reconstructed Orlando Magic, winning 105-99.
Caron Butler scored 20 points and Dirk Nowitzki had 17 to help the Mavericks pull away in the fourth quarter for their 16th win in 17 games. A night after ending Miami's 12-game streak, Dallas shot 50 percent from the floor, including 46 percent from 3-point range.
The Magic have lost their first two games since Gilbert Arenas, Jason Richardson and Hedo Turkoglu were acquired on Saturday, and eight of their past nine.
Dwight Howard had 26 points and 23 rebounds but got little help from teammates.
In Charlotte, Oklahoma City overcame a poor shooting night by dominating the fourth quarter in a victory over reeling Charlotte.
The Thunder entered the final period trailing 69-68, but responded with a 25-3 run. The Bobcats missed their first 11 shots, committed five turnovers and didn't get their first field goal until 2:52 remained, producing sarcastic cheers.
Oklahoma's Kevin Durant scored 32 points, hitting 14-of-16 free throws and adding seven rebounds.
Stephen Jackson scored 20 points for the Bobcats, who dropped their fourth straight as coach Larry Brown continues to question their effort.
In Chicago, the home team beat Philadelphia for its eighth win in nine games.
Despite missing big men Joakim Noah and Taj Gibson, Chicago dominated nearly every offensive category and recorded its most lopsided win of the season.
Derrick Rose and Luol Deng each scored 22 points. Rose also had 12 assists for his seventh double double.
Andre Iguodala scored 17 points for Philadelphia.
In Memphis, New Jersey snapped a 10-game road losing skid by beating Memphis.
Brook Lopez scored 26 points and Sasha Vujacic added a season-high 16. Lopez was 8 of 14 from the field, and missed only one of his 11 free throws.
The Nets outrebounded Memphis 49-39.
Marc Gasol scored 19 points to lead the Grizzlies.
Warriors 117, Kings 109, OT: In Sacramento, Monta Ellis scored nine of his 36 points in overtime to lift Golden State over struggling Sacramento.
The Warriors, who had lost 14 of their previous 16 games, rallied from a 16-point deficit in the fourth quarter to force overtime.
Reggie Williams scored 24 points for Golden State.
Beno Udrih scored a career-high 34 points for the Kings, who have lost six straight.
