Antetokounmpo scored a game-high 32 points in the 129-105 loss Monday at Staples Center in Los Angeles. Leonard also had nine rebounds, eight assists and two steals for the Clippers, who are on a six-game winning streak.
The Clippers made 19 3-pointers in the victory and shot 53.7% from the floor.
"We are going to need everyone to win a basketball game, not just me," Leonard told reporters. "We are just as good as our weakest link."
Antetokounmpo and Jrue Holiday scored 12 points apiece in the first 12 minutes to help the Bucks earn a 38-26 lead at the end of the first quarter.
The Clippers then went on a 9-0 run to cut the Bucks lead to three points in the second quarter. They later took a lead in the quarter and the teams exchanged momentum until Nicolas Batum made a late 3-pointer to give the Clippers a 57-55 lead at the break.
Antetokounmpo tied the game for the Bucks at the start of the third quarter, but the Clippers answered with an 8-0 run. The Clippers held a 96-86 edge going into the final frame. They added another 11-0 run midway through the fourth quarter to push the lead to 119-100.
Clippers guard Luke Kennard scored 12 points down the stretch to secure the victory.
Kennard totaled 21 points and made 5 of 6 3-point attempts in the win. Fellow Clippers guard Reggie Jackson chipped in 20 points. Terance Mann had 14 points off the Clippers bench.
Holiday scored 24 points and had seven assists for the Bucks. Bucks forward Khris Middleton had 15 points in the loss.