Leonard also had six steals, five assists and three rebounds in the win. Fellow Clippers All-Star Paul George chipped in 19 points and 12 assists.
"We are just trying to get better," Leonard told reporters. "That's our mindset. We aren't complacent about where we are right now. We are going to keep it moving."
Kings guard De'Aaron Fox had 17 points through two quarters before the Los Angeles outscored Sacramento 54-40 down the stretch. The game featured 12 lead changes and was tied seven times.
Leonard scored 10 points over the first 12 minutes, but the Kings held a 29-25 lead after the first quarter. Fox responded with 14 points in the second quarter, but the Clippers outscored the Kings 36-27 in the frame to earn a 61-56 lead at halftime.
In the third, the Clippers went on a 14-2 run to push their lead to 80-63 and ended the quarter with a 12-3 run for a 95-75 edge at the start of the final frame. Los Angeles tightened its defense down the stretch to hold onto the victory.
Nicolas Batum and Ivica Zubac scored 11 points apiece for the Clippers. Zubac also recorded 12 rebounds.
Fox led the Kings with 25 points and seven assists. Glenn Robinson III scored 14 points off the Kings bench. Buddy Hield scored 13 points in the loss.
The Kings have now lost four-consecutive games.
"Everybody is hungry for a win," Fox said. "Sometimes just one win can turn the whole thing around. We are just fighting for that and take it one game at a time."