Brooklyn ended a four-game losing streak and won for only the 10th time this season. That leaves six teams in the NBA with fewer than 10 wins this year -- New York, Philadelphia, Milwaukee, Orlando, Utah and Sacramento.
Livingston scored 20 points after having produced just 19 during his last six games combined.
The Nets took a 13-point lead after one period and led by 16 heading into the closing quarter.
Brooklyn will now go on a three-game road trip against three of the best teams in the league -- Indiana, San Antonio and Oklahoma City.
Milwaukee, which has lost seven out of eight, came up with a career-best 16 points from Giannis Antetokounmpo.
Larry Sanders returned to the Milwaukee lineup after missing 25 games with a broken right thumb. He scored 10 points and grabbed seven rebounds before fouling out.