James Harden had 30 points and 10 assists, and Paul George scored 18 for the Clippers.
Trae Young, the Eastern Conference player of the week, had 25 points and De’Andre Hunter matched a season high with 27 off the bench for the Hawks, who had won four in a row.
The Clippers went 6-1 on a 13-day trip and improved to 26-5 since Nov. 30. They won at Miami on Sunday, the front end of this back-to-back.
“To go 6-1 against the caliber of teams we played on this trip, coming into it, we knew tonight was going to be tough,” coach Tyronn Lue said. “Got down early in the second half, continued to keep fighting. It was a total team effort.”
The Clippers shot 60% from three-point range, while the Hawks finished at 51.3%. The 149 points were the Clippers’ second-most of the season. They only turned the ball over seven times.
“Taking care of the basketball has always been a big key for us,” Lue said. “We are too good offensively to turn it over. If we get shots up, we’re going to be pretty good.”
Leonard, the Western Conference player of the week, keyed an 8-2 burst with under 2:30 to play, hitting a three-pointer, converting a three-point play and assisting on a layup. The run gave the Clippers a 139-130 lead.
After three free throws by Young, Harden banked in a three while being fouled and stretched the lead to 142-133 with 1:06 left.
Lue was disappointed the Clippers permitted 43 points in the fourth quarter.
“We’ve got to get back home and be better (on defense),” he said. “I don’t know if it was fatigue. Guys have played a lot of games, a lot of minutes. I’ll give them a little bit of a break with that, but we have to be better. We had some slippage, so we have to get home and clean this stuff up.”
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A back-and-forth third quarter ended with a buzzer-beating three by Daniel Theis that gave the Clippers a 102-101 edge entering the fourth.
Young tied the score at 66 with a driving hoop in the final second of the second period.
Hawks center Clint Capela, who has started 47 games, sat out with a left adductor strain and will be re-evaluated in seven to 10 days.
Clippers starting center Ivica Zubac also missed the game after being listed as questionable. Zubac has a right calf strain.
Up next for the Clippers: vs. the New Orleans Pelicans at Crypto.com Arena on Wednesday.