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.
Extracted and lightly reformatted for readability. · Source: pt