The victory was a costly one, however, since the Clippers All-Star point guard Chris Paul suffered a shoulder injury in the third period that team officials said would keep him out of action for up to five weeks.
Paul fell on the shoulder as he came off a screen. He went to the locker room immediately and did not return.
Dallas, coming off a 3-0 road trip, took a 110-103 lead when Shawn Marion hit a jumper with 4:08 to play. The Mavericks managed just two more points the rest of the way and surrendered the lead for good on a 3-point play by Griffin with 1:37 left.
Griffin and DeAndre Jordan both scored 25 points with Jordan adding 18 rebounds and Griffin recording 15. Paul had scored 19 points when he was injured.
Dirk Nowitzki paced Dallas with 24 points and Marion contributed 20.
Los Angeles, which is making a quick weekend trip through Texas, has won three out of four. The Clippers will face San Antonio Saturday.