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Navarro, seeded 23rd, broke the hard-hitting Belarusian for a fourth time on match point to book a quarterfinal clash with ninth seed Maria Sakkari of Greece.
Sabelnka beat fourth seed Coco Gauff in a thriller on while Zheng got the better of Ukrainian qualifier Dayana Yastremska.
Gauff set up a semifinal clash with Sabalenka in a rematch of last year's US Open final.
The top remaining seed after Saturday's early exit for world No. 1 Iga Swiatek, Sabalenka's biggest enemy has often been her own emotions but she continued to keep them strictly under control to reach the last eight without dropping a set.
The second semifinal between Swiatek and top seed Sabalenka was cancelled for the night due to rain.
Swiatek will next face Sabalenka in the semifinals, while Gauff will lock horns with Pegula for a place in the final.
All four players in the group can reach the semifinals.
The win completed a remarkable turnaround for Gauff, who was left distraught after a first round exit at Wimbledon in July.
Sabalenka will try to heap even more disappointment on US tennis fans in Saturday's final when she takes on Coco Gauff.
Coco Gauff won the final 10 games of her match against Elise Mertens, completing a 3-6, 6-3, 6-0 comeback