Both players scored 36 in the thrilling clash, however, two clutch three-point efforts from Landry Shamet proved to be just enough for the Clippers to end the Mavs' four-game winning streak.
After Los Angeles took an 11-point lead into half-time, Dallas bounced back strongly in the third quarter thanks to an explosion from Doncic, who finished one assist short of a triple-double.
But Shamet's late buckets, combined with four missed free throws by the Mavericks within the last minute of play, sealed the three-point victory for the Clippers.
Leonard also had 11 rebounds in the victory, while Kristaps Porzingis was kept relatively quiet in his return from injury, finishing with just 10 points and nine boards.
The win sees the Clippers overtake the Denver Nuggets to return to second spot in the Western Conference.