The world No. 1 saved two break points at 4:4 in the decider before closing out a 4-hour, 12-minute classic under the Ashe lights.
Iga Świątek extended her winning streak to 14 matches with a 7:5, 6:2 victory, converting five of seven break points.
Novak Djokovic will climb to world No. 3 on Monday regardless of the semifinal outcome, passing Alexander Zverev.
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