Memphis steadily pulled away in the second half, building a 17-point lead midway through the fourth period while handing the Lakers their fourth straight loss.
Los Angeles has dropped seven consecutive road games for the first time in eight seasons.
The Grizzlies outrebounded Los Angeles 52-34 and allowed the Lakers just three second-chance points.
Kobe Bryant managed 29 points for the Lakers, but Dwight Howard left the game after playing 14 minutes with what appeared to be a shoulder injury. He went 0-of-4 from the floor and scored two free throws.
Los Angeles has won just twice in the month of January and is eight games below .500.