The match ended in dramatic fashion when both Mertens and Sabalenka were drawn into the net and Barty sent a lob over both their heads.
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Spain’s Nadal, 33, won 7-5 6-3 5-7 4-6 6-4 against the fifth seed in New York.
The win was an upset which also put the brakes on the American’s bid to equal the all-time record
Since returning to action after the birth of her first child Williams has come agonisingly close to matching Margaret Court’s mark three times and will have a chance on Saturday to do so in front of an adoring home crowd for a second successive year.
But the three-time champion will also be defending the honour of the big-three in men’s tennis.
Schwartzman may have been the smallest player in 25 years to reach the US Open quarterfinals but gave Nadal a big fight and forced the Spaniard to grind out a win
The 20-time grand slam winner had looked destined for a box-office final against Rafael Nadal in what would have been the great rivals’ first meeting at Flushing Meadows.
It was the American’s 100th career victory at the US Open and at 44 minutes was the match quickest at this year’s tournament.
Rafael Nadal came through his first stern examination at the US Open to move a step closer to a maiden Flushing Meadows meeting with Roger Federer.
Schwartzman had not been on court for more than two hours in any of his previous matches.
The second-seeded Spaniard was in cruise control as he took the first set behind some superb serving and stout defence, but the big-hitting Croatian battled back to snatch the second.
Williams however recovered to advance to the US Open quarter-finals.
Defending champion Naomi Osaka dominated rising star Coco Gauff 6-3 6-0 to reach the last 16 of the US Open.
Townsend fought back from losing the opening set to record a shock 2-6, 6-3, 7-6 win over the Romanian at Flushing Meadows in New York.
The 15-year-old wildcard Gauff overcame world no 112 Babos after two hours and 21 minutes of play, becoming the youngest woman to reach the last 32 at Flushing Meadows since Anna Kournikova’s run in 1996.
Novak Djokovic needed extensive treatment on a shoulder injury during his second-round win over Juan Ignacio Londero at the US Open.
Trailing 5-3 in the second set, seven-times Grand Slam champion Williams saved five-match points to hold serve in a dramatic 22-point game
Borna Coric withdrew from the US Open on Wednesday ahead of the 12th seed’s second-round match against Grigor Dimitrov due to a lower back strain, the tournament organisers said.
The Greek later said he was struggling for inspiration in his game.
Millman delivered the upset of the tournament last year when he beat five-times winner Roger Federer in a surprising run to the quarter-finals but he was unable to recreate the same magic against the relentless Spanish second seed.