All the signs before the match pointed to a comfortable Swiatek win.
She had lost only five games in her previous three Grand Slam matches – including a 6-0 6-0 victory over Amanda Anisimova in July’s Wimbledon final – and had won 14 successive sets at the majors.
US Open debutant Lamens, meanwhile, had not been beyond the second round of a Grand Slam before.
That gulf was evident early on, with Lamens failing to hit a single winner in the opening set.
But Swiatek, who won the Cincinnati Open in the build-up to Flushing Meadows, lost her way in set two.
The six-time Grand Slam champion and her coaching team began to show the frustration of some wayward groundstrokes, which contributed to a match total of 29 unforced errors.
Swiatek, though, regained some control in the decider and shrugged off handing back one of her breaks of serve to set up a tie with Kalinskaya.