This is the first time World No. 1 Djokovic, who continues his quest for a historic Golden Grand Slam in the singles this week, has played mixed doubles at the Olympics.
The Serbian pair did not face a break point on their way to victory and will next face Kevin Krawietz and Laura Siegemund after the Germans beat American team Bethanie Mattek-Sands and Rajeev Ram 6-4, 5-7, 10-8.
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Stefanos Tsitsipas got over his singles disappointment by teaming with Maria Sakkari to beat Canadian tandem Gabriela Dabrowski and Felix Auger-Aliassime 6-3, 6-4. Tsitsipas and Sakkari play Barty and Peers in the last eight.
There was success for the ROC on Wednesday. Anastasia Pavlyuchenkova and Andrey Rublev moved through with a 5-7, 6-4, 11-9 victory against Croatian pair Darija Jurak and Ivan Dodig, while Elena Vesnina and Aslan Karatsev raced past French duo Kristina Mladenovic and Nicolas Mahut 6-4, 6-2.