Cleveland scored the final five points of the contest after Los Angeles had closed within two with 20 seconds remaining on a 3-point play from Blake Griffin.
Antawn Jamison led Cleveland with 27 points and eight rebounds, while Ramon Sessions had 24 points and 13 assists in his first start of the season.
Sessions filled in for rookie Kyrie Irving, who suffered a concussion Tuesday in a loss to Miami.
Griffin produced 25 points and grabbed 15 rebounds for the Clippers, who had won six of their previous seven games. Chris Paul had 16 points and 12 assists.
Kenyon Martin made his season debut for Los Angeles and scored six points. Martin played in China during the NBA lockout and had to wait until the end of his team's season before he could play again in the United States.
Cleveland took a 13-point lead in the third period thanks to a 17-4 run.