The Australian Open champion converted three of her four break point opportunities and saved the two break points she faced during the 74-minute match in Louis Armstrong Stadium.
Sabalenka, who can claim the top ranking for the first time if she advances one round further than Iga Swiatek (22) in New York, used a steady stream of power from the backhand and forehand sides to overwhelm world number 96 Burrage.
The Belarusian second seed consolidated an early break for a 3-0 lead and while Burrage responded with holds to love on her next two service games Sabalenka leaned on her own serve to seal the opening set.
Sabalenka was barely tested in the second set where she hit a forehand winner to go up a double break before closing it out with a hold to love.
Up next for Sabalenka will be a clash against Frenchwoman Clara Burel (22), a 6-4 6-2 winner over Czech 25th seed Karolina Pliskova (31).