The Hawks shot 51 percent from the field to end a two-game skid.
Millsap added nine rebounds to his 25 points and Korver hit six from beyond the 3-point arc among his 23 points. Al Horford tacked on 21 and nine rebounds.
Atlanta converted 12-of-23 attempts from 3-point range.
The contest was the opener of a seven-game road trip for the Clippers, who will be in Memphis Thursday. Los Angeles has dropped two straight.
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