Bazemore scored 15 points and Brooks had 14, including 10 in the fourth quarter, in their debut for the struggling Lakers, who ended an eight-game home losing streak.
The pair was acquired by the Lakers on Thursday in a trade with in-state rival Golden State. They led a solid attack by the Los Angeles bench, which outscored the Celtics reserves 63-21 and accounted for the final 44 points scored by the Lakers as a team.
Veteran Pau Gasol, who survived this week's trading deadline. added 16 points and seven rebounds for the Lakers.
Los Angles put on a pedestrian performance for the first three quarters before erupting in the fourth. They outscored Boston 38-18 in the final period and wound up shooting 48.2 percent from the floor compared to 39.2 percent for the Bostonians.