Darius Garland added 15 points and 11 assists and Derrick Jones Jr. 13 points for Los Angeles, which made 45 of 77 shots (58.4 per cent).
Former Raptor Gary Trent Jr. had a season-high 36 points to pace Milwaukee, which had only eight players available. Taurean Prince added 18 points and AJ Green scored 15 for the Bucks, who have lost 10 of their last 12 games.
The Bucks stayed close early, trailing 29-25 after one quarter with Trent scoring 11 points, including sinking three of five from three-point range.
The Clippers began to pull away in the second, holding a 57-46 lead at the half after leading by as many as 16. Leonard, the former Raptors star, had 15 first-half points.
Brook Lopez, a member of the Bucks’ 2021 NBA championship team, was honored with a video tribute in his first visit back to Milwaukee. He was whistled for a technical foul as the teams were headed to the locker room at halftime.
Los Angeles outscored Milwaukee 39-28 in the third and extended its lead to as many as 24 points in the fourth before the Bucks pulled within 11 in the late stages.
Sloppy play hurt Milwaukee, which committed 22 turnovers leading to 33 Clippers points.
Giannis Antetokounmpo sat out a seventh consecutive game for Milwaukee with a left knee hyperextension and bone bruise. The two-time MVP has played in a career-low 36 games this season.
The Bucks also were missing Kevin Porter Jr. (right knee), Bobby Portis (left wrist sprain), Kyle Kuzma (Achilles tendinopathy), Ryan Rollins (left hip flexor), Myles Turner (right knee), Gary Harris (personal reasons) and Thanasis Antetokounmpo (left calf).
Green and Ousmane Dieng fouled out in the fourth, leaving the Bucks with six available players to finish the game.
Clippers: Host the Portland Trail Blazers on Tuesday.
Bucks: Host the Dallas Mavericks on Tuesday.
