Milwaukee ended a four-game skid and improved its hold on the final playoff position in the Eastern Conference.
Los Angeles, however, now has only a half-game advantage over Utah in the race for the last post-season spot in the West.
Sanders scored 21 points and grabbed 13 rebounds, helping the Bucks bounce back from a seven-point deficit after one period. The Bucks pulled away late after the Lakers held a one-point lead with just over 9 minutes to play.
The Bucks are seven full games in front of Philadelphia for the eighth seed in the playoff chase.
Kobe Bryant had 30 points for the Lakers, moving him within four of tying Wilt Chamberlain for the fourth spot on the NBA's career scoring list.
Bryant, however, went just 6-of-17 from the field while the Lakers were losing for the fourth time in five games.