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All four players can still qualify from Red Group after Belinda Bencic's three-set victory over Petra Kvitova in the later match.
The Japanese world No. 3's place in the tournament will now be taken by alternate Kiki Bertens of the Netherlands.
The push comes just under two weeks after devastating attacks on Saudi Arabia's oil infrastructure.
Serena Williams had the chance to equal Margaret Court's all-time record but instead it was Canadian teenager Bianca Andreescu who grabbed the trophy with a 6-3, 7-5 win.
Williams, a six-time US Open winner, romped to a 6-3, 6-4 victory over Croatian 22nd seed Petra Martic to set up a quarter-final with China's Wang Qiang, the conqueror of world number two Barty.
Djokovic, champion in four of the past five Slams and 16 overall, was less bothered by left shoulder pain that nagged him in the second round in defeating 111th-ranked American Denis Kudla 6-3, 6-4, 6-2.
Ashleigh Barty overwhelmed British wild card Harriet Dart 6-1, 6-1.
Barty could face former champion Garbine Muguruza in the third round and awaiting in the quarterfinals could be defending champion Angelique Kerber or seven-time winner Serena Williams with twice champion Petra Kvitova a potential obstacle in the semifinal.
Konta, who had never before won a match here, will face either Petra Martic or Marketa Vondrousova for a spot in the final.
The powerful Czech struggled throughout to find the range on her feared serve and forehand as 31st seed Martic matched her best performance by reaching the last 16.