Despite battling foul trouble, Brand made seven of 11 shots and grabbed six rebounds. He scored five points during a 13-0 run the Clippers used to open the third quarter and take the lead for good.
Odom also scored five points during the run and finished with 14 points, 11 rebounds, three assists and two blocks. Olowokandi scored 13 points and pulled down 11 rebounds.
Eric Piatkowski had 16 points and made three of six three-pointers for the Clippers, who hit six of 16 from long range. Quentin Richardson added 15 points and nine rebounds as Los Angeles held a 54-40 rebounding edge.
Los Angeles outscored Dallas, 38-18, in the third quarter. The Clippers had a 13-point lead late in the period, but Dallas rallied in the final 12 minutes.
The Mavs chipped away throughout the fourth quarter and Dirk Nowitzki's three-pointer with 1:39 left made it 99-96. But Dallas committed a 24-second violation and missed two jumpers in the final 11 seconds.
Nowitzki finished with 21 points and seven rebounds. Michael Finley scored 18 points and Juwan Howard added 14 and 10 rebounds.