Forward Dirk Nowitzki led Dallas with 27 points and eight rebounds. Center Samuel Dalembert added 20 points and seven rebounds. Guards Jose Calderon had 16 points, and Monta Ellis had 13 points and 13 assists.
Barnes nailed back-to-back 3-pointers to give Los Angeles a 100-91 advantage with 2:47 remaining in the third, but Dallas scored 15 consecutive points for a 106-100 lead two minutes into the fourth quarter.
Dallas (23-17) continued to pour it on with a 23-4 surge, capped by a three-point play by reserve center Brandan Wright with 4:49 remaining in the game that made it 123-106. That is when the Clippers launched their rally.
Los Angeles owned a 76-64 lead early in the third quarter after an alley-oop dunk by center DeAndre Jordan, but the Mavericks put together a 19-8 run capped by a dunk by forward Shawn Marion to pull to within 84-83 midway through the quarter.
Tempers flared in the first half when Griffin and Dalembert got tangled up beneath the Clippers' basket and had to be restrained. Dalembert received a technical foul.
NOTES: The Clippers are nearing a deal with free agent F Hedo Turkoglu, coach Doc Rivers said. Turkoglu is expected to join the club before it embarks on a seven-game road trip beginning Friday against the New York Knicks. Turkoglu's addition will probably result in the release of G Maalik Wayns or G Darius Morris, both of whom recently signed 10-day contracts. ... ... Injured Mavericks PG Devin Harris is close to making his season debut. Harris, who has been out with a toe injury, did not play against Los Angeles and has been ruled out of Friday night's game against the Phoenix Suns. He could play possibly Saturday at Dallas against the Portland Trail Blazers. ... In five games starting in place of injured PG Chris Paul, Los Angeles PG Darren Collison is averaging 16.6 points and 7.2 assists.