When Sabalenka lifted the Miami Open trophy in April, she established a 3,000-point lead at the top of the world rankings.
But early exits – by her high standards at least – followed at the French Open and Wimbledon. Now, Australian Open champion Elena Rybakina, who faces American wildcard Thea Frodin on Tuesday, trails her by just 434 points.
It means that Sabalenka, who is defending 2,000 points at Flushing Meadows, will have to win the title and hope Rybakina falls before the semi-finals to extend her 99-week reign as world number one.
Home favourites Jessica Pegula and Coco Gauff could also secure the number one ranking with a title triumph.
Should Sabalenka win a third successive US Open title, she would become only the third woman to do so in the Open era after Serena Williams and Chris Evert.
However, she will need to improve considerably to navigate a stacked draw in New York.
Sabalenka stormed through the first set against the 52nd-ranked Osorio but struggled in the second, landing 48% of her first serves and hitting 12 unforced errors.
But the four-time major singles champion fended off three break points and struck decisively at 4-4 before serving out victory after one hour and 28 minutes.
Sabalenka will face Russian qualifier Polina Iatcenko next.
Later on Monday, American Amanda Anisimova celebrated her 25th birthday with a dominant 6-1 6-3 win against compatriot Ashlyn Krueger.
The crowd on Louis Armstrong treated the 10th seed, who was runner-up to Sabalenka at last year’s US Open, with a rendition of ‘happy birthday’ afterwards.
Six-time major champion Iga Swiatek, who won the title in 2022 but is seeded eighth after a below-par season, made a solid start with a 6-2 6-3 victory over China’s Wang Xiyu.
Wimbledon champion Linda Noskova made it safely through with a 7-5 6-1 win over American Katie Volynets, while Karolina Muchova, who lost to Noskova in the SW19 final, dropped just three games in a 58-minute demolition of Austria’s Sinja Kraus.
French Open finalist Maja Chwalinska was less fortunate as she fell to a 6 2 6-3 defeat by home hope Taylor Townsend.