Parker also dished off 12 assists, while Kawhi Leonard and Tiago Splitter chipped in with 14 points each as the Spurs broke a three-game road losing streak.
They won without the services of veteran Tim Duncan, who was rested during the second of back-to-back games.
The skidding Hawks, meanwhile, lost for the eighth time in 10 games on a day they were told guard Lou Williams would miss the rest of the season with a torn knee ligament.
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