After Kobe Bryant asked the Staples Center crowd for a moment of silence, the Lakers took out their longtime rivals by 14 points, improving to 26-29 on the season.
Dwight Howard led the Lakers with 24 points and 12 rebounds in a dominant shooting performance (10 of 13).
The Lakers shot 50.6% from the field and 71% from the free-throw line (22 of 31). Boston took 20 free throws, making 12.
The Celtics kept the game close early while shooting 45% from three-point range but ultimately fell to 28-26 in defeat.
The Lakers doubled up Boston on the offensive glass, 14-7, winning the overall rebounding battle, 49-34. Clark collected a career-high 16 rebounds.
Bryant and Nash led the Lakers with seven assists apiece.
The Lakers next host the Portland Trail Blazers on Friday night.
The Lakers extended their lead to 19 in the third quarter. Boston closed the gap slightly to 14 on Avery Bradley's tip-in with 0.9 seconds left in the quarter.
Dwight Howard led the Lakers with 22 point and 11 rebounds, although he had five turnovers. Earl Clark and Antawn Jamison climbed into double figures with 10 apiece as the Lakers shot 53.1% from the field.
Both Kobe Bryant and Howard were given technical fouls for arguing calls in the third quarter.
The Lakers are neutralizing a big night from Paul Pierce to hold onto their nine-point lead at halftime.
Pierce scored 23 points on nine-of-15 shooting, including four of seven from three-point range. The Celtics shot 49% from the field and 50% from behind the arc (six of 12) and yet the Lakers held on.