The second seed had arrived in New York as the form player in the women's game after following up her Wimbledon triumph with victory in the Cincinnati Open and she had looked every inch the tournament favourite with her opening demolition job on Emiliana Arango.
But on Thursday, it proved a much more trying day for the Pole as she made a host of errors to lose the second set before regrouping and coming through 6-1 4-6 6-4.
From 4-3 up in the second set after a one-sided first stanza, Swiatek had tightened up to lose four games in a row as Lamens, ranked 66, forced a decider.
She also fought back when going 4-1 down but Swiatek kept her nerve to set up a third-round contest against 29th seed Anna Kalinskaya.
"It wasn't an easy match and I made some mistakes. I'm happy that at the end I could be more proactive," said Swiatek.
"I probably got a little tight in the second set and she used the opportunity and was using her chances. It was not easy, but the third set is a reset."
Elsewhere, Japan's four-time major winner Naomi Osaka looked in fine fettle as she overwhelmed American Hailey Baptiste 6-3 6-1 with a dominant performance.
The two-time US Open champion had not reached the third round at Flushing Meadows since 2021 but looked very comfortable as she booked a meeting with either Australian 15th seed Daria Kasatkina or Kamilla Rakhimova.
"I was just really trying to focus and not give her any free points and just be positive," said Osaka, who donned a sparkling purple kit and walked in with her Labubu charm she nicknamed "Arthur Flash" in honour of late American tennis pioneer Arthur Ashe.
Osaka, who has shown glimpses of her old form this year especially after reaching the Montreal final, said: "I was really stressed the entire time ... I'm really excited to be moving better."
With agencies
